Chapter 12.3, Problem 95AYU

To determine

To find: The choice which results in more money is better.

Answer to Problem 95AYU

The second choice results in more money.

Explanation of Solution

Given information:

Choice A: 1000, 999, 998, ……………….(1000 terms)

Choice B: 1, 2, 4, ………………………(19 terms)

Calculation:

Calculate the value $S_{1000}$ .

Use formula: $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$

  $\begin{array}{c}{S}_{1000}=\frac{1000}{2}\left[2(1000)+(1000-1)(-1)\right]\\ =500\times 1001\\ =500,500\end{array}$

Calculate the value of $S_{19}^{/}$

Use formula: $S_n=\frac{a\left(r^n-1\right)}{r-1}$

  $\begin{array}{c}{S}_{19}^{/}=\frac{1\left(2^{19}-1\right)}{2-1}\\ =2^{19}-1\\ =524,287\end{array}$

Therefore, the second choice results in more money.