Chapter 12.3, Problem 47AYU

To determine

To find: The sum of the geometric sequence using graphing utility.

Answer to Problem 47AYU

The sum of the geometric sequence using graphing utility is $1.995432683$ .

Explanation of Solution

Given information:

The geometric sequence is

  ${{\displaystyle \sum _{n=1}^{15}\left(\frac{2}{3}\right)}}^n$

Calculation:

Consider the geometric sequence as

  ${{\displaystyle \sum _{n=1}^{15}\left(\frac{2}{3}\right)}}^n$

The first term of the sequence is

  $a_1=\frac{2}{3}$

The common ratio of the sequence is

  $\begin{array}{c}r=\frac{a_2}{a_1}\\ =\frac{{\left(\frac{2}{3}\right)}^2}{{\left(\frac{2}{3}\right)}^1}\\ =\frac{2}{3}\end{array}$

The number of terms is

  $n=15$

Use the scientific calculator (graphing utility) to calculate the sum of the geometric sequence is

  

Therefore, the sum of the geometric sequence using graphing utility is $1.995432683$ .