Question

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

$\sum _{n=1}^{15}4·3^{n-1}$

Short answer

The sum of the given sequence is$28697812$

Step-by-step solution

Step 1. Write the given information.

The given sequence is$\sum _{n=1}^{15}4·3^{n-1}$

Step 2. Find the sum.

$a_1=4,r=3,n=15$

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

$$\begin{gathered} s_{15}=\frac{4(3^{15}-1)}{3-1} \\ =\frac{4(3^{15}-1)}{2} \\ =2·(3^{15}-1) \\ =28697812 \end{gathered}$$