Question

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

$\frac{3}{9}+\frac{3^2}{9}+\frac{3^3}{9}+...+\frac{3^{15}}{9}$

Short answer

The sum of the given sequence is$2391484.3$

Step-by-step solution

Step 1. Write the given information.

The given sequence is$\frac{3}{9}+\frac{3^2}{9}+\frac{3^3}{9}+...+\frac{3^{15}}{9}$

Step 2. Find the common ratio.

$$\begin{gathered} a_1=\frac{3}{9},a_2=\frac{3^2}{9}n=15 \\ \frac{a_2}{a_1}=\frac{{\displaystyle \frac{3^2}{9}}}{{\displaystyle \frac{3}{9}}} \\ =3 \\ r=3 \end{gathered}$$

Step 4. Find the sum.

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

$$\begin{gathered} s_{15}=\frac{3}{9}·\frac{3^{15}-1}{3-1} \\ =\frac{3^{15}-1}{6} \\ =2391484.3 \end{gathered}$$