Question

In Problems 39– 44, find each sum.

$\sum _{k=1}^{n}4·3^{k-1}$

Short answer

The sum of the given sequence is$2·(3^n-1)$

Step-by-step solution

Step 1. Write the given information.

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

Step 2. Find the sum.

$a_1=4,r=3$

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

$$\begin{gathered} s_n=\frac{4(3^n-1)}{3-1} \\ =\frac{4(3^n-1)}{2} \\ =2·(3^n-1) \end{gathered}$$