Chapter 12: Q 45. (page 825)

For Problems 45–50, use a graphing utility to find the sum of each geometric sequence.
$\frac{1}{4} + \frac{2}{4} + \frac{2^{2}}{4} + \frac{2^{3}}{4} + . . . + \frac{2^{14}}{4}$

Short Answer

Expert verified

The sum of the given sequence is $8191.75$

Step by step solution

Step 1. Write the given information.

The given sequence is $\frac{1}{4} + \frac{2}{4} + \frac{2^{2}}{4} + \frac{2^{3}}{4} + . . . + \frac{2^{14}}{4}$

Step 2. Find the common ratio.

$a_{1} = \frac{1}{4}, a_{2} = \frac{2}{4}, n = 15 \frac{a_{2}}{a_{1}} = \frac{\frac{2}{4}}{\frac{1}{4}} = 2 r = 2$

Step 3. Find the sum.

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

$s_{15} = \frac{\frac{1}{4} (2^{15} - 1)}{2 - 1} = \frac{32768 - 1}{4} = 8191.75$

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For Problems 45–50, use a graphing utility to find the sum of each geometric sequence.
$\frac{1}{4} + \frac{2}{4} + \frac{2^{2}}{4} + \frac{2^{3}}{4} + . . . + \frac{2^{14}}{4}$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Find the common ratio.

Step 3. Find the sum.

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For Problems 45–50, use a graphing utility to find the sum of each geometric sequence.14+24+224+234+...+2144

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Find the common ratio.

Step 3. Find the sum.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Statistics

Logic and Functions

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

For Problems 45–50, use a graphing utility to find the sum of each geometric sequence.
$\frac{1}{4} + \frac{2}{4} + \frac{2^{2}}{4} + \frac{2^{3}}{4} + . . . + \frac{2^{14}}{4}$