{"id":2190,"date":"2025-08-07T17:59:25","date_gmt":"2025-08-07T17:59:25","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&p=2190"},"modified":"2026-02-03T15:19:48","modified_gmt":"2026-02-03T15:19:48","slug":"sequences-get-stronger","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/sequences-get-stronger\/","title":{"raw":"Sequences: Get Stronger","rendered":"Sequences: Get Stronger"},"content":{"raw":"

Sequences and Their Notations<\/h2>\r\nFor the following exercises, write the first four terms of the sequence.\r\n\r\n7. [latex]{a}_{n}=-\\frac{16}{n+1}[\/latex]\r\n\r\n11. [latex]{a}_{n}=1.25\\cdot {\\left(-4\\right)}^{n - 1}[\/latex]\r\n\r\n13. [latex]{a}_{n}=\\frac{{n}^{2}}{2n+1}[\/latex]\r\n\r\nFor the following exercises, write an explicit formula for each sequence.\r\n\r\n21. [latex]4, 7, 12, 19, 28,\\dots [\/latex]\r\n\r\n23. [latex]1,1,\\frac{4}{3},2,\\frac{16}{5},\\dots [\/latex]\r\n\r\n25. [latex]1,-\\frac{1}{2},\\frac{1}{4},-\\frac{1}{8},\\frac{1}{16},\\dots [\/latex]\r\n\r\nFor the following exercises, write the first five terms of the sequence.\r\n\r\n27. [latex]{a}_{1}=3,\\text{ }{a}_{n}=\\left(-3\\right){a}_{n - 1}[\/latex]\r\n\r\n29. [latex]{a}_{1}=-1,\\text{ }{a}_{n}=\\frac{{\\left(-3\\right)}^{n - 1}}{{a}_{n - 1}-2}[\/latex]\r\n\r\nFor the following exercises, write a recursive formula for each sequence.\r\n\r\n35. [latex]-8,-6,-3,1,6,\\dots [\/latex]\r\n\r\n37. [latex]35,\\text{ }38,\\text{ }41,\\text{ }44,\\text{ }47,\\text{ }\\dots [\/latex]\r\n\r\nFor the following exercises, write the first four terms of the sequence.\r\n\r\n43. [latex]{a}_{n}=\\frac{n!}{{n}^{\\text{2}}}[\/latex]\r\n\r\n45. [latex]{a}_{n}=\\frac{n!}{{n}^{2}-n - 1}[\/latex]\r\n\r\nFor the following exercises, write a recursive formula for the sequence using the first five points shown on the graph.\r\n\r\n55.\r\n\"Graph\r\n\r\n67. Consider the sequence defined by [latex]{a}_{n}=-6 - 8n[\/latex]. Is [latex]{a}_{n}=-421[\/latex] a term in the sequence? Verify the result.\r\n

Arithmetic Sequences<\/h2>\r\n1. What is an arithmetic sequence?\r\n\r\n3. How do we determine whether a sequence is arithmetic?\r\n\r\nFor the following exercises, determine whether the sequence is arithmetic. If so find the common difference.\r\n\r\n7. [latex]\\left\\{0,\\frac{1}{2},1,\\frac{3}{2},2,...\\right\\}[\/latex]\r\n\r\n9. [latex]\\left\\{4,16,64,256,1024,...\\right\\}[\/latex]\r\n\r\nFor the following exercises, write the first five terms of the arithmetic sequence.\r\n\r\n11. [latex]{a}_{1}=0[\/latex] , [latex]d=\\frac{2}{3}[\/latex]\r\n\r\n13. [latex]{a}_{13}=-60,{a}_{33}=-160[\/latex]\r\n\r\nFor the following exercises, find the specified term for the arithmetic sequence.\r\n\r\n15. First term is 4, common difference is 5, find the 4th<\/sup> term.\r\n\r\n17. First term is 6, common difference is 7, find the 6th<\/sup> term.\r\n\r\n19. Find the first term or [latex]{a}_{1}[\/latex] of an arithmetic sequence if [latex]{a}_{6}=12[\/latex] and [latex]{a}_{14}=28[\/latex].\r\n\r\n21. Find the first term or [latex]{a}_{1}[\/latex] of an arithmetic sequence if [latex]{a}_{8}=40[\/latex] and [latex]{a}_{23}=115[\/latex].\r\n\r\n23. Find the first term or [latex]{a}_{1}[\/latex] of an arithmetic sequence if [latex]{a}_{11}=11[\/latex] and [latex]{a}_{21}=16[\/latex].\r\n\r\nFor the following exercises, find the first five terms of the arithmetic sequence.\r\n\r\n27. [latex]{a}_{1}=-19;\\text{ }{a}_{n}={a}_{n - 1}-1.4[\/latex]\r\n\r\n41. [latex]{a}_{n}=24 - 4n[\/latex]\r\n\r\nFor the following exercises, write a recursive formula for each arithmetic sequence.\r\n\r\n29. [latex]{a}_{n}=\\left\\{17,26,35,...\\right\\}[\/latex]\r\n\r\n33. [latex]{a}_{n}=\\left\\{8.9,10.3,11.7,...\\right\\}[\/latex]\r\n\r\n35. [latex]{a}_{n}=\\left\\{\\frac{1}{5},\\frac{9}{20},\\frac{7}{10},...\\right\\}[\/latex]\r\n\r\n37. [latex]{a}_{n}=\\left\\{\\frac{1}{6},-\\frac{11}{12},-2,...\\right\\}[\/latex]\r\n\r\nFor the following exercises, write an explicit formula for each arithmetic sequence.\r\n\r\n45. [latex]{a}_{n}=\\left\\{-5\\text{, }95\\text{, }195\\text{, }...\\right\\}[\/latex]\r\n\r\n49. [latex]{a}_{n}=\\left\\{15.8,18.5,21.2,...\\right\\}[\/latex]\r\n\r\n51. [latex]{a}_{n}=\\left\\{0,\\frac{1}{3},\\frac{2}{3},...\\right\\}[\/latex]\r\n\r\nFor the following exercises, find the number of terms in the given finite arithmetic sequence.\r\n\r\n53. [latex]{a}_{n}=\\left\\{3\\text{,}-4\\text{,}-11\\text{, }...\\text{,}-60\\right\\}[\/latex]\r\n\r\n55. [latex]{a}_{n}=\\left\\{\\frac{1}{2},2,\\frac{7}{2},...,8\\right\\}[\/latex]\r\n

Geometric Sequences<\/h2>\r\n1. What is a geometric sequence?\r\n\r\n3. What is the procedure for determining whether a sequence is geometric?\r\n\r\nFor the following exercises, determine whether the sequence is geometric. If so, find the common ratio.\r\n\r\n7. [latex]-0.125,0.25,-0.5,1,-2,..[\/latex].\r\n\r\n9. [latex]-6,-12,-24,-48,-96,..[\/latex].\r\n\r\n11. [latex]-1,\\frac{1}{2},-\\frac{1}{4},\\frac{1}{8},-\\frac{1}{16},..[\/latex].\r\n\r\n13. [latex]0.8,4,20,100,500,..[\/latex].\r\n\r\nFor the following exercises, write the first five terms of the geometric sequence.\r\n\r\n15. [latex]\\begin{array}{cc}{a}_{1}=5,& r=\\frac{1}{5}\\end{array}[\/latex]\r\n\r\n17. [latex]\\begin{array}{cc}{a}_{6}=25,& {a}_{8}\\end{array}=6.25[\/latex]\r\n\r\n23. [latex]\\begin{array}{cc}{a}_{1}=7,& {a}_{n}=0.2{a}_{n - 1}\\end{array}[\/latex]\r\n\r\n33. [latex]{a}_{n}=12\\cdot {\\left(-\\frac{1}{2}\\right)}^{n - 1}[\/latex]\r\n\r\nFor the following exercises, find the specified term for the geometric sequence.\r\n\r\n19. The first term is 16 and the common ratio is [latex]-\\frac{1}{3}[\/latex]. Find the 4th<\/sup> term.\r\n\r\n21. [latex]{a}_{n}=\\left\\{-2,\\frac{2}{3},-\\frac{2}{9},\\frac{2}{27},...\\right\\}[\/latex]. Find [latex]{a}_{7}[\/latex].\r\n\r\n43. Let [latex]{a}_{n}=-{\\left(-\\frac{1}{3}\\right)}^{n - 1}[\/latex]. Find [latex]{a}_{12}[\/latex].\r\n\r\nFor the following exercises, write a recursive formula for each geometric sequence.\r\n\r\n25. [latex]{a}_{n}=\\left\\{-32,-16,-8,-4,...\\right\\}[\/latex]\r\n\r\n27. [latex]{a}_{n}=\\left\\{10,-3,0.9,-0.27,...\\right\\}[\/latex]\r\n\r\n29. [latex]{a}_{n}=\\left\\{\\frac{3}{5},\\frac{1}{10},\\frac{1}{60},\\frac{1}{360},...\\right\\}[\/latex]\r\n\r\n31. [latex]{a}_{n}=\\left\\{\\frac{1}{512},-\\frac{1}{128},\\frac{1}{32},-\\frac{1}{8},...\\right\\}[\/latex]\r\n\r\nFor the following exercises, write an explicit formula for each geometric sequence.\r\n\r\n35. [latex]{a}_{n}=\\left\\{1,3,9,27,...\\right\\}[\/latex]\r\n\r\n37. [latex]{a}_{n}=\\left\\{0.8,-4,20,-100,...\\right\\}[\/latex]\r\n\r\n39. [latex]{a}_{n}=\\left\\{-1,-\\frac{4}{5},-\\frac{16}{25},-\\frac{64}{125},...\\right\\}[\/latex]\r\n\r\n41. [latex]{a}_{n}=\\left\\{3,-1,\\frac{1}{3},-\\frac{1}{9},...\\right\\}[\/latex]\r\n\r\nFor the following exercises, find the number of terms in the given finite geometric sequence.\r\n\r\n45. [latex]{a}_{n}=\\left\\{2,1,\\frac{1}{2},...,\\frac{1}{1024}\\right\\}[\/latex]\r\n\r\n51. Use recursive formulas to give two examples of geometric sequences whose 3rd<\/sup> terms are [latex]200[\/latex].\r\n\r\n53. Find the 5th<\/sup> term of the geometric sequence [latex]\\left\\{b,4b,16b,...\\right\\}[\/latex].\r\n

Series and Their Notations<\/h2>\r\n1. What is an [latex]n\\text{th}[\/latex] partial sum?\r\n\r\n3. What is a geometric series?\r\n\r\nFor the following exercises, write the series using summation notation.\r\n\r\n7. The sum from of [latex]n=0[\/latex]\u00a0to [latex]n=4[\/latex]\u00a0of [latex]5n[\/latex]\r\n\r\n9. The sum that results from adding the number 4 five times\r\n\r\n11. [latex]10+18+26+\\dots +162[\/latex]\r\n\r\n17. [latex]8+4+2+\\dots +0.125[\/latex]\r\n\r\nFor the following exercises, use the formula for the sum of the first [latex]n[\/latex] terms of each arithmetic sequence.\r\n\r\n13. [latex]\\frac{3}{2}+2+\\frac{5}{2}+3+\\frac{7}{2}[\/latex]\r\n\r\n15. [latex]3.2+3.4+3.6+\\dots +5.6[\/latex]\r\n\r\n35. [latex]6+\\frac{15}{2}+9+\\frac{21}{2}+12+\\frac{27}{2}+15[\/latex]\r\n\r\n37. [latex]\\sum _{k=1}^{11}\\left(\\frac{k}{2}-\\frac{1}{2}\\right)[\/latex]\r\n\r\nFor the following exercises, use the formula for the sum of the first [latex]n[\/latex] terms of each geometric sequence, and then state the indicated sum.\r\n\r\n19. [latex]9+3+1+\\frac{1}{3}+\\frac{1}{9}[\/latex]\r\n\r\n21. [latex]\\sum _{a=1}^{11}64\\cdot {0.2}^{a - 1}[\/latex]\r\n\r\n39. [latex]{S}_{7}[\/latex] for the series [latex]0.4 - 2+10 - 50..[\/latex].\r\n\r\n41. [latex]\\sum _{n=1}^{10}-2\\cdot {\\left(\\frac{1}{2}\\right)}^{n - 1}[\/latex]\r\n\r\nFor the following exercises, determine whether the infinite series has a sum. If so, write the formula for the sum. If not, state the reason.\r\n\r\n23. [latex]2+1.6+1.28+1.024+..[\/latex].\r\n\r\n25. [latex]\\sum_{k=1}^{\\infty}-{\\left(-\\frac{1}{2}\\right)}^{k - 1}[\/latex]\r\n\r\nFor the following exercises, find the indicated sum.\r\n\r\n31. [latex]\\sum _{n=1}^{6}n\\left(n - 2\\right)[\/latex]\r\n\r\n33. [latex]\\sum _{k=1}^{7}{2}^{k}[\/latex]\r\n\r\nFor the following exercises, find the sum of the infinite geometric series.\r\n\r\n43. [latex]-1-\\frac{1}{4}-\\frac{1}{16}-\\frac{1}{64}..[\/latex].\r\n\r\n45. [latex]\\sum _{n=1}^{\\infty }4.6\\cdot {0.5}^{n - 1}[\/latex]\r\n\r\nFor the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.\r\n\r\n47. Deposit amount: $150; total deposits: [latex]24[\/latex]; interest rate: [latex]3%[\/latex], compounded monthly\r\n\r\n49. Deposit amount:\u00a0$100; total deposits: [latex]120[\/latex]; interest rate: [latex]10%[\/latex], compounded semi-annually\r\n\r\n57. Karl has two years to save [latex]$10,000[\/latex] to buy a used car when he graduates. To the nearest dollar, what would his monthly deposits need to be if he invests in an account offering a 4.2% annual interest rate that compounds monthly?\r\n\r\n59. A boulder rolled down a mountain, traveling 6 feet in the first second. Each successive second, its distance increased by 8 feet. How far did the boulder travel after 10 seconds?\r\n\r\n61. A pendulum travels a distance of 3 feet on its first swing. On each successive swing, it travels [latex]\\frac{3}{4}[\/latex] the distance of the previous swing. What is the total distance traveled by the pendulum when it stops swinging?","rendered":"

Sequences and Their Notations<\/h2>\n

For the following exercises, write the first four terms of the sequence.<\/p>\n

7. [latex]{a}_{n}=-\\frac{16}{n+1}[\/latex]<\/p>\n

11. [latex]{a}_{n}=1.25\\cdot {\\left(-4\\right)}^{n - 1}[\/latex]<\/p>\n

13. [latex]{a}_{n}=\\frac{{n}^{2}}{2n+1}[\/latex]<\/p>\n

For the following exercises, write an explicit formula for each sequence.<\/p>\n

21. [latex]4, 7, 12, 19, 28,\\dots[\/latex]<\/p>\n

23. [latex]1,1,\\frac{4}{3},2,\\frac{16}{5},\\dots[\/latex]<\/p>\n

25. [latex]1,-\\frac{1}{2},\\frac{1}{4},-\\frac{1}{8},\\frac{1}{16},\\dots[\/latex]<\/p>\n

For the following exercises, write the first five terms of the sequence.<\/p>\n

27. [latex]{a}_{1}=3,\\text{ }{a}_{n}=\\left(-3\\right){a}_{n - 1}[\/latex]<\/p>\n

29. [latex]{a}_{1}=-1,\\text{ }{a}_{n}=\\frac{{\\left(-3\\right)}^{n - 1}}{{a}_{n - 1}-2}[\/latex]<\/p>\n

For the following exercises, write a recursive formula for each sequence.<\/p>\n

35. [latex]-8,-6,-3,1,6,\\dots[\/latex]<\/p>\n

37. [latex]35,\\text{ }38,\\text{ }41,\\text{ }44,\\text{ }47,\\text{ }\\dots[\/latex]<\/p>\n

For the following exercises, write the first four terms of the sequence.<\/p>\n

43. [latex]{a}_{n}=\\frac{n!}{{n}^{\\text{2}}}[\/latex]<\/p>\n

45. [latex]{a}_{n}=\\frac{n!}{{n}^{2}-n - 1}[\/latex]<\/p>\n

For the following exercises, write a recursive formula for the sequence using the first five points shown on the graph.<\/p>\n

55.
\n\"Graph<\/p>\n

67. Consider the sequence defined by [latex]{a}_{n}=-6 - 8n[\/latex]. Is [latex]{a}_{n}=-421[\/latex] a term in the sequence? Verify the result.<\/p>\n

Arithmetic Sequences<\/h2>\n

1. What is an arithmetic sequence?<\/p>\n

3. How do we determine whether a sequence is arithmetic?<\/p>\n

For the following exercises, determine whether the sequence is arithmetic. If so find the common difference.<\/p>\n

7. [latex]\\left\\{0,\\frac{1}{2},1,\\frac{3}{2},2,...\\right\\}[\/latex]<\/p>\n

9. [latex]\\left\\{4,16,64,256,1024,...\\right\\}[\/latex]<\/p>\n

For the following exercises, write the first five terms of the arithmetic sequence.<\/p>\n

11. [latex]{a}_{1}=0[\/latex] , [latex]d=\\frac{2}{3}[\/latex]<\/p>\n

13. [latex]{a}_{13}=-60,{a}_{33}=-160[\/latex]<\/p>\n

For the following exercises, find the specified term for the arithmetic sequence.<\/p>\n

15. First term is 4, common difference is 5, find the 4th<\/sup> term.<\/p>\n

17. First term is 6, common difference is 7, find the 6th<\/sup> term.<\/p>\n

19. Find the first term or [latex]{a}_{1}[\/latex] of an arithmetic sequence if [latex]{a}_{6}=12[\/latex] and [latex]{a}_{14}=28[\/latex].<\/p>\n

21. Find the first term or [latex]{a}_{1}[\/latex] of an arithmetic sequence if [latex]{a}_{8}=40[\/latex] and [latex]{a}_{23}=115[\/latex].<\/p>\n

23. Find the first term or [latex]{a}_{1}[\/latex] of an arithmetic sequence if [latex]{a}_{11}=11[\/latex] and [latex]{a}_{21}=16[\/latex].<\/p>\n

For the following exercises, find the first five terms of the arithmetic sequence.<\/p>\n

27. [latex]{a}_{1}=-19;\\text{ }{a}_{n}={a}_{n - 1}-1.4[\/latex]<\/p>\n

41. [latex]{a}_{n}=24 - 4n[\/latex]<\/p>\n

For the following exercises, write a recursive formula for each arithmetic sequence.<\/p>\n

29. [latex]{a}_{n}=\\left\\{17,26,35,...\\right\\}[\/latex]<\/p>\n

33. [latex]{a}_{n}=\\left\\{8.9,10.3,11.7,...\\right\\}[\/latex]<\/p>\n

35. [latex]{a}_{n}=\\left\\{\\frac{1}{5},\\frac{9}{20},\\frac{7}{10},...\\right\\}[\/latex]<\/p>\n

37. [latex]{a}_{n}=\\left\\{\\frac{1}{6},-\\frac{11}{12},-2,...\\right\\}[\/latex]<\/p>\n

For the following exercises, write an explicit formula for each arithmetic sequence.<\/p>\n

45. [latex]{a}_{n}=\\left\\{-5\\text{, }95\\text{, }195\\text{, }...\\right\\}[\/latex]<\/p>\n

49. [latex]{a}_{n}=\\left\\{15.8,18.5,21.2,...\\right\\}[\/latex]<\/p>\n

51. [latex]{a}_{n}=\\left\\{0,\\frac{1}{3},\\frac{2}{3},...\\right\\}[\/latex]<\/p>\n

For the following exercises, find the number of terms in the given finite arithmetic sequence.<\/p>\n

53. [latex]{a}_{n}=\\left\\{3\\text{,}-4\\text{,}-11\\text{, }...\\text{,}-60\\right\\}[\/latex]<\/p>\n

55. [latex]{a}_{n}=\\left\\{\\frac{1}{2},2,\\frac{7}{2},...,8\\right\\}[\/latex]<\/p>\n

Geometric Sequences<\/h2>\n

1. What is a geometric sequence?<\/p>\n

3. What is the procedure for determining whether a sequence is geometric?<\/p>\n

For the following exercises, determine whether the sequence is geometric. If so, find the common ratio.<\/p>\n

7. [latex]-0.125,0.25,-0.5,1,-2,..[\/latex].<\/p>\n

9. [latex]-6,-12,-24,-48,-96,..[\/latex].<\/p>\n

11. [latex]-1,\\frac{1}{2},-\\frac{1}{4},\\frac{1}{8},-\\frac{1}{16},..[\/latex].<\/p>\n

13. [latex]0.8,4,20,100,500,..[\/latex].<\/p>\n

For the following exercises, write the first five terms of the geometric sequence.<\/p>\n

15. [latex]\\begin{array}{cc}{a}_{1}=5,& r=\\frac{1}{5}\\end{array}[\/latex]<\/p>\n

17. [latex]\\begin{array}{cc}{a}_{6}=25,& {a}_{8}\\end{array}=6.25[\/latex]<\/p>\n

23. [latex]\\begin{array}{cc}{a}_{1}=7,& {a}_{n}=0.2{a}_{n - 1}\\end{array}[\/latex]<\/p>\n

33. [latex]{a}_{n}=12\\cdot {\\left(-\\frac{1}{2}\\right)}^{n - 1}[\/latex]<\/p>\n

For the following exercises, find the specified term for the geometric sequence.<\/p>\n

19. The first term is 16 and the common ratio is [latex]-\\frac{1}{3}[\/latex]. Find the 4th<\/sup> term.<\/p>\n

21. [latex]{a}_{n}=\\left\\{-2,\\frac{2}{3},-\\frac{2}{9},\\frac{2}{27},...\\right\\}[\/latex]. Find [latex]{a}_{7}[\/latex].<\/p>\n

43. Let [latex]{a}_{n}=-{\\left(-\\frac{1}{3}\\right)}^{n - 1}[\/latex]. Find [latex]{a}_{12}[\/latex].<\/p>\n

For the following exercises, write a recursive formula for each geometric sequence.<\/p>\n

25. [latex]{a}_{n}=\\left\\{-32,-16,-8,-4,...\\right\\}[\/latex]<\/p>\n

27. [latex]{a}_{n}=\\left\\{10,-3,0.9,-0.27,...\\right\\}[\/latex]<\/p>\n

29. [latex]{a}_{n}=\\left\\{\\frac{3}{5},\\frac{1}{10},\\frac{1}{60},\\frac{1}{360},...\\right\\}[\/latex]<\/p>\n

31. [latex]{a}_{n}=\\left\\{\\frac{1}{512},-\\frac{1}{128},\\frac{1}{32},-\\frac{1}{8},...\\right\\}[\/latex]<\/p>\n

For the following exercises, write an explicit formula for each geometric sequence.<\/p>\n

35. [latex]{a}_{n}=\\left\\{1,3,9,27,...\\right\\}[\/latex]<\/p>\n

37. [latex]{a}_{n}=\\left\\{0.8,-4,20,-100,...\\right\\}[\/latex]<\/p>\n

39. [latex]{a}_{n}=\\left\\{-1,-\\frac{4}{5},-\\frac{16}{25},-\\frac{64}{125},...\\right\\}[\/latex]<\/p>\n

41. [latex]{a}_{n}=\\left\\{3,-1,\\frac{1}{3},-\\frac{1}{9},...\\right\\}[\/latex]<\/p>\n

For the following exercises, find the number of terms in the given finite geometric sequence.<\/p>\n

45. [latex]{a}_{n}=\\left\\{2,1,\\frac{1}{2},...,\\frac{1}{1024}\\right\\}[\/latex]<\/p>\n

51. Use recursive formulas to give two examples of geometric sequences whose 3rd<\/sup> terms are [latex]200[\/latex].<\/p>\n

53. Find the 5th<\/sup> term of the geometric sequence [latex]\\left\\{b,4b,16b,...\\right\\}[\/latex].<\/p>\n

Series and Their Notations<\/h2>\n

1. What is an [latex]n\\text{th}[\/latex] partial sum?<\/p>\n

3. What is a geometric series?<\/p>\n

For the following exercises, write the series using summation notation.<\/p>\n

7. The sum from of [latex]n=0[\/latex]\u00a0to [latex]n=4[\/latex]\u00a0of [latex]5n[\/latex]<\/p>\n

9. The sum that results from adding the number 4 five times<\/p>\n

11. [latex]10+18+26+\\dots +162[\/latex]<\/p>\n

17. [latex]8+4+2+\\dots +0.125[\/latex]<\/p>\n

For the following exercises, use the formula for the sum of the first [latex]n[\/latex] terms of each arithmetic sequence.<\/p>\n

13. [latex]\\frac{3}{2}+2+\\frac{5}{2}+3+\\frac{7}{2}[\/latex]<\/p>\n

15. [latex]3.2+3.4+3.6+\\dots +5.6[\/latex]<\/p>\n

35. [latex]6+\\frac{15}{2}+9+\\frac{21}{2}+12+\\frac{27}{2}+15[\/latex]<\/p>\n

37. [latex]\\sum _{k=1}^{11}\\left(\\frac{k}{2}-\\frac{1}{2}\\right)[\/latex]<\/p>\n

For the following exercises, use the formula for the sum of the first [latex]n[\/latex] terms of each geometric sequence, and then state the indicated sum.<\/p>\n

19. [latex]9+3+1+\\frac{1}{3}+\\frac{1}{9}[\/latex]<\/p>\n

21. [latex]\\sum _{a=1}^{11}64\\cdot {0.2}^{a - 1}[\/latex]<\/p>\n

39. [latex]{S}_{7}[\/latex] for the series [latex]0.4 - 2+10 - 50..[\/latex].<\/p>\n

41. [latex]\\sum _{n=1}^{10}-2\\cdot {\\left(\\frac{1}{2}\\right)}^{n - 1}[\/latex]<\/p>\n

For the following exercises, determine whether the infinite series has a sum. If so, write the formula for the sum. If not, state the reason.<\/p>\n

23. [latex]2+1.6+1.28+1.024+..[\/latex].<\/p>\n

25. [latex]\\sum_{k=1}^{\\infty}-{\\left(-\\frac{1}{2}\\right)}^{k - 1}[\/latex]<\/p>\n

For the following exercises, find the indicated sum.<\/p>\n

31. [latex]\\sum _{n=1}^{6}n\\left(n - 2\\right)[\/latex]<\/p>\n

33. [latex]\\sum _{k=1}^{7}{2}^{k}[\/latex]<\/p>\n

For the following exercises, find the sum of the infinite geometric series.<\/p>\n

43. [latex]-1-\\frac{1}{4}-\\frac{1}{16}-\\frac{1}{64}..[\/latex].<\/p>\n

45. [latex]\\sum _{n=1}^{\\infty }4.6\\cdot {0.5}^{n - 1}[\/latex]<\/p>\n

For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.<\/p>\n

47. Deposit amount: $150; total deposits: [latex]24[\/latex]; interest rate: [latex]3%[\/latex], compounded monthly<\/p>\n

49. Deposit amount:\u00a0$100; total deposits: [latex]120[\/latex]; interest rate: [latex]10%[\/latex], compounded semi-annually<\/p>\n

57. Karl has two years to save [latex]$10,000[\/latex] to buy a used car when he graduates. To the nearest dollar, what would his monthly deposits need to be if he invests in an account offering a 4.2% annual interest rate that compounds monthly?<\/p>\n

59. A boulder rolled down a mountain, traveling 6 feet in the first second. Each successive second, its distance increased by 8 feet. How far did the boulder travel after 10 seconds?<\/p>\n

61. A pendulum travels a distance of 3 feet on its first swing. On each successive swing, it travels [latex]\\frac{3}{4}[\/latex] the distance of the previous swing. What is the total distance traveled by the pendulum when it stops swinging?<\/p>\n","protected":false},"author":67,"menu_order":27,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":156,"module-header":"practice","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2190"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":6,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2190\/revisions"}],"predecessor-version":[{"id":5508,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2190\/revisions\/5508"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/156"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2190\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2190"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2190"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2190"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}