{"id":2077,"date":"2015-11-12T18:30:42","date_gmt":"2015-11-12T18:30:42","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=2077"},"modified":"2015-11-12T18:30:42","modified_gmt":"2015-11-12T18:30:42","slug":"solutions-13","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/solutions-13\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"

Solutions to Try Its<\/h2>\n1.\u00a038\n\n2.\u00a0[latex]\\text{26}\\text{.4}[\/latex]\n\n3.\u00a0[latex]\\text{328}[\/latex]\n\n4.\u00a0[latex]\\text{-280}[\/latex]\n\n5.\u00a0$2,025\n\n6.\u00a0[latex]\\approx 2,000.00[\/latex]\n\n7.\u00a09,840\n\n8.\u00a0$275,513.31\n\n9.\u00a0The sum is defined. It is geometric.\n\n10.\u00a0The sum of the infinite series is defined.\n\n11.\u00a0The sum of the infinite series is defined.\n\n12.\u00a03\n\n13.\u00a0The series is not geometric.\n\n14. [latex]-\\frac{3}{11}[\/latex]\n\n15.\u00a0$92,408.18\n

Solutions to Odd-Numbered Exercises<\/h2>\n1.\u00a0An [latex]n\\text{th}[\/latex] partial sum is the sum of the first [latex]n[\/latex] terms of a sequence.\n\n3.\u00a0A geometric series is the sum of the terms in a geometric sequence.\n\n5.\u00a0An annuity is a series of regular equal payments that earn a constant compounded interest.\n\n7.\u00a0[latex]\\sum _{n=0}^{4}5n[\/latex]\n\n9.\u00a0[latex]\\sum _{k=1}^{5}4[\/latex]\n\n11.\u00a0[latex]\\sum _{k=1}^{20}8k+2[\/latex]\n\n13.\u00a0[latex]{S}_{5}=\\frac{5\\left(\\frac{3}{2}+\\frac{7}{2}\\right)}{2}[\/latex]\n\n15.\u00a0[latex]{S}_{13}=\\frac{13\\left(3.2+5.6\\right)}{2}[\/latex]\n\n17.\u00a0[latex]\\sum _{k=1}^{7}8\\cdot {0.5}^{k - 1}[\/latex]\n\n19.\u00a0[latex]{S}_{5}=\\frac{9\\left(1-{\\left(\\frac{1}{3}\\right)}^{5}\\right)}{1-\\frac{1}{3}}=\\frac{121}{9}\\approx 13.44[\/latex]\n\n21.\u00a0[latex]{S}_{11}=\\frac{64\\left(1-{0.2}^{11}\\right)}{1 - 0.2}=\\frac{781,249,984}{9,765,625}\\approx 80[\/latex]\n\n23.\u00a0The series is defined. [latex]S=\\frac{2}{1 - 0.8}[\/latex]\n\n25.\u00a0The series is defined. [latex]S=\\frac{-1}{1-\\left(-\\frac{1}{2}\\right)}[\/latex]\n\n27.\n\"Graph\n\n29.\u00a0Sample answer: The graph of [latex]{S}_{n}[\/latex] seems to be approaching 1. This makes sense because [latex]\\sum _{k=1}^{\\infty }{\\left(\\frac{1}{2}\\right)}^{k}[\/latex] is a defined infinite geometric series with [latex]S=\\frac{\\frac{1}{2}}{1-\\left(\\frac{1}{2}\\right)}=1[\/latex].\n\n31.\u00a049\n\n33.\u00a0254\n\n35.\u00a0[latex]{S}_{7}=\\frac{147}{2}[\/latex]\n\n37.\u00a0[latex]{S}_{11}=\\frac{55}{2}[\/latex]\n\n39.\u00a0[latex]{S}_{7}=5208.4[\/latex]\n\n41.\u00a0[latex]{S}_{10}=-\\frac{1023}{256}[\/latex]\n\n43.\u00a0[latex]S=-\\frac{4}{3}[\/latex]\n\n45.\u00a0[latex]S=9.2[\/latex]\n\n47.\u00a0$3,705.42\n\n49.\u00a0$695,823.97\n\n51.\u00a0[latex]{a}_{k}=30-k[\/latex]\n\n53.\u00a09 terms\n\n55.\u00a0[latex]r=\\frac{4}{5}[\/latex]\n\n57.\u00a0$400 per month\n\n59.\u00a0420 feet\n\n61.\u00a012 feet","rendered":"

Solutions to Try Its<\/h2>\n

1.\u00a038<\/p>\n

2.\u00a0[latex]\\text{26}\\text{.4}[\/latex]<\/p>\n

3.\u00a0[latex]\\text{328}[\/latex]<\/p>\n

4.\u00a0[latex]\\text{-280}[\/latex]<\/p>\n

5.\u00a0$2,025<\/p>\n

6.\u00a0[latex]\\approx 2,000.00[\/latex]<\/p>\n

7.\u00a09,840<\/p>\n

8.\u00a0$275,513.31<\/p>\n

9.\u00a0The sum is defined. It is geometric.<\/p>\n

10.\u00a0The sum of the infinite series is defined.<\/p>\n

11.\u00a0The sum of the infinite series is defined.<\/p>\n

12.\u00a03<\/p>\n

13.\u00a0The series is not geometric.<\/p>\n

14. [latex]-\\frac{3}{11}[\/latex]<\/p>\n

15.\u00a0$92,408.18<\/p>\n

Solutions to Odd-Numbered Exercises<\/h2>\n

1.\u00a0An [latex]n\\text{th}[\/latex] partial sum is the sum of the first [latex]n[\/latex] terms of a sequence.<\/p>\n

3.\u00a0A geometric series is the sum of the terms in a geometric sequence.<\/p>\n

5.\u00a0An annuity is a series of regular equal payments that earn a constant compounded interest.<\/p>\n

7.\u00a0[latex]\\sum _{n=0}^{4}5n[\/latex]<\/p>\n

9.\u00a0[latex]\\sum _{k=1}^{5}4[\/latex]<\/p>\n

11.\u00a0[latex]\\sum _{k=1}^{20}8k+2[\/latex]<\/p>\n

13.\u00a0[latex]{S}_{5}=\\frac{5\\left(\\frac{3}{2}+\\frac{7}{2}\\right)}{2}[\/latex]<\/p>\n

15.\u00a0[latex]{S}_{13}=\\frac{13\\left(3.2+5.6\\right)}{2}[\/latex]<\/p>\n

17.\u00a0[latex]\\sum _{k=1}^{7}8\\cdot {0.5}^{k - 1}[\/latex]<\/p>\n

19.\u00a0[latex]{S}_{5}=\\frac{9\\left(1-{\\left(\\frac{1}{3}\\right)}^{5}\\right)}{1-\\frac{1}{3}}=\\frac{121}{9}\\approx 13.44[\/latex]<\/p>\n

21.\u00a0[latex]{S}_{11}=\\frac{64\\left(1-{0.2}^{11}\\right)}{1 - 0.2}=\\frac{781,249,984}{9,765,625}\\approx 80[\/latex]<\/p>\n

23.\u00a0The series is defined. [latex]S=\\frac{2}{1 - 0.8}[\/latex]<\/p>\n

25.\u00a0The series is defined. [latex]S=\\frac{-1}{1-\\left(-\\frac{1}{2}\\right)}[\/latex]<\/p>\n

27.
\n\"Graph<\/p>\n

29.\u00a0Sample answer: The graph of [latex]{S}_{n}[\/latex] seems to be approaching 1. This makes sense because [latex]\\sum _{k=1}^{\\infty }{\\left(\\frac{1}{2}\\right)}^{k}[\/latex] is a defined infinite geometric series with [latex]S=\\frac{\\frac{1}{2}}{1-\\left(\\frac{1}{2}\\right)}=1[\/latex].<\/p>\n

31.\u00a049<\/p>\n

33.\u00a0254<\/p>\n

35.\u00a0[latex]{S}_{7}=\\frac{147}{2}[\/latex]<\/p>\n

37.\u00a0[latex]{S}_{11}=\\frac{55}{2}[\/latex]<\/p>\n

39.\u00a0[latex]{S}_{7}=5208.4[\/latex]<\/p>\n

41.\u00a0[latex]{S}_{10}=-\\frac{1023}{256}[\/latex]<\/p>\n

43.\u00a0[latex]S=-\\frac{4}{3}[\/latex]<\/p>\n

45.\u00a0[latex]S=9.2[\/latex]<\/p>\n

47.\u00a0$3,705.42<\/p>\n

49.\u00a0$695,823.97<\/p>\n

51.\u00a0[latex]{a}_{k}=30-k[\/latex]<\/p>\n

53.\u00a09 terms<\/p>\n

55.\u00a0[latex]r=\\frac{4}{5}[\/latex]<\/p>\n

57.\u00a0$400 per month<\/p>\n

59.\u00a0420 feet<\/p>\n

61.\u00a012 feet<\/p>\n\n\t\t\t

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