Question

For Problems 45–50, use a graphing utility to find the sum of each geometric sequence.

$-1-2-4-8-...-2^{14}$

Short answer

The sum of the given sequence is$-32767$$-32767$

Step-by-step solution

Step 1. Write the given information.

The given sequence is$-1-2-4-8-...-2^{14}$

Step 2. Find the common ratio.

$$\begin{gathered} a_1=-1,a_2=-2,n=15 \\ \frac{a_2}{a_1}=\frac{-2}{-1} \\ =2 \\ r=2 \end{gathered}$$

Step 3. Find the sum.

The formula for the sum of nth term is$s_n=\frac{a_1(r^n-1)}{r-1}$

$$\begin{gathered} s_{15}=-1·\frac{2^{15}-1}{2-1} \\ =-(2^{15}-1) \\ =-32767 \end{gathered}$$