13.4E: Series and Their Notations (Exercises)

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21. Use summation notation to write the sum of terms $\frac{1}{2} m+5$ from $m=0$ to $m=5$.

22. Use summation notation to write the sum that results from adding the number 13 twenty times.

23. Use the formula for the sum of the first $n$ terms of an arithmetic series to find the sum of the first eleven terms of the arithmetic series $2.5,4,5.5, \ldots$

24. A ladder has 15 tapered rungs, the lengths of which increase by a common difference. The first rung is 5 inches long, and the last rung is 20 inches long. What is the sum of the lengths of the rungs?

25. Use the formula for the sum of the first $n$ terms of a geometric series to find $S_{9}$ for the series $12,6,3, \frac{3}{2}, \ldots$

26. The fees for the first three years of a hunting club membership are given in Table 1 . If fees continue to rise at the same rate, how much will the total cost be for the first ten years of membership?

Table 1
Year	Membership Fees
1	$1500
2	$1950
3	$2535

27. Find the sum of the infinite geometric series $\sum_{k=1}^{\infty} 45 \cdot\left(-\frac{1}{3}\right)^{k-1}$.

28. A ball has a bounce-back ratio of $\frac{3}{5}$ the height of the previous bounce. Write a series representing the total distance traveled by the ball, assuming it was initially dropped from a height of 5 feet. What is the total distance? (Hint: the total distance the ball travels on each bounce is the sum of the heights of the rise and the fall.).
29. Alejandro deposits $\$ 80$ of his monthly earnings into an annuity that earns $6.25 \%$ annual interest, compounded monthly. How much money will he have saved after 5 years?

30. The twins Sarah and Scott both opened retirement accounts on their $21^{\text {st }}$ birthday. Sarah deposits $\$ 4,800.00$ each year, earning $5.5 \%$ annual interest, compounded monthly. Scott deposits $\$ 3,600.00$ each year, earning $8.5 \%$ annual interest, compounded monthly. Which twin will earn the most interest by the time they are 55 years old? How much more?