Chapter 12.3, Problem 45AYU

To determine

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

Answer to Problem 45AYU

The sum of the geometric sequence using graphing utility is $8191.75$ .

Explanation of Solution

Given information:

The geometric sequence is

  $\frac{1}{4}+\frac{2}{4}+\frac{2^2}{4}+\frac{2^3}{4}+\mathrm{....}+\frac{2^{14}}{4}$

Calculation:

Consider the geometric sequence as

  $\frac{1}{4}+\frac{2}{4}+\frac{2^2}{4}+\frac{2^3}{4}+\mathrm{....}+\frac{2^{14}}{4}$

The first term of the sequence is

  $\begin{array}{c}{a}_1=a\\ =\frac{1}{4}\end{array}$

The common ratio of the sequence is

  $r=2$

The number of terms is

  $n=15$

Use the graphing utility to calculate the sum of the geometric sequence.

  

Therefore, the sum of the geometric sequence using graphing utility is $8191.75$ .