Solutions to Try Its

1. 38

2. $\text{26}\text{.4}$

3. $\text{328}$

4. $\text{-280}$

5. $2,025

6. $\approx 2,000.00$

7. 9,840

8. $275,513.31

9. The sum is defined. It is geometric.

10. The sum of the infinite series is defined.

11. The sum of the infinite series is defined.

12. 3

13. The series is not geometric.

14. $-\frac{3}{11}$

15. $92,408.18

Solutions to Odd-Numbered Exercises

1. An $n\text{th}$ partial sum is the sum of the first $n$ terms of a sequence.

3. A geometric series is the sum of the terms in a geometric sequence.

5. An annuity is a series of regular equal payments that earn a constant compounded interest.

7. $\sum _{n=0}^{4}5n$

9. $\sum _{k=1}^{5}4$

11. $\sum _{k=1}^{20}8k+2$

13. ${S}_{5}=\frac{5\left(\frac{3}{2}+\frac{7}{2}\right)}{2}$

15. ${S}_{13}=\frac{13\left(3.2+5.6\right)}{2}$

17. $\sum _{k=1}^{7}8\cdot {0.5}^{k - 1}$

19. ${S}_{5}=\frac{9\left(1-{\left(\frac{1}{3}\right)}^{5}\right)}{1-\frac{1}{3}}=\frac{121}{9}\approx 13.44$

21. ${S}_{11}=\frac{64\left(1-{0.2}^{11}\right)}{1 - 0.2}=\frac{781,249,984}{9,765,625}\approx 80$

23. The series is defined. $S=\frac{2}{1 - 0.8}$

25. The series is defined. $S=\frac{-1}{1-\left(-\frac{1}{2}\right)}$

27.

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

31. 49

33. 254

35. ${S}_{7}=\frac{147}{2}$

37. ${S}_{11}=\frac{55}{2}$

39. ${S}_{7}=5208.4$

41. ${S}_{10}=-\frac{1023}{256}$

43. $S=-\frac{4}{3}$

45. $S=9.2$

47. $3,705.42

49. $695,823.97

51. ${a}_{k}=30-k$

53. 9 terms

55. $r=\frac{4}{5}$

57. $400 per month

59. 420 feet

61. 12 feet