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Chapter 12: Q 48. (page 825)

For Problems 45–50, use a graphing utility to find the sum of each geometric sequence.
$\sum_{n = 1}^{15} 4 \cdot 3^{n - 1}$

Short Answer

Expert verified

The sum of the given sequence is $28697812$

Step by step solution

01

Step 1. Write the given information.

The given sequence is $\sum_{n = 1}^{15} 4 \cdot 3^{n - 1}$

02

Step 2. Find the sum.

$a_{1} = 4, r = 3, n = 15$

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

$s_{15} = \frac{4 (3^{15} - 1)}{3 - 1} = \frac{4 (3^{15} - 1)}{2} = 2 \cdot (3^{15} - 1) = 28697812$

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Most popular questions from this chapter

Problems 17–28, write down the first five terms of each sequence.

$\{c_{n}\} = \{{(- 1)}^{n + 1} n^{2}\}$

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.

$a_{1} = 1; a_{2} = 2; a_{n} = a_{n - 1} \cdot a_{n - 2}$

In Problems 51–66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

$6 + 2 + \frac{2}{3} + . . . . .$

In Problems 61–70, express each sum using summation notation.

$a + a r + a r^{2} + . . . . . + a r^{n - 1}$

In Problems 71-82, find the sum of each sequence.

${\sum k^{3}}_{k = 4}^{24}$

See all solutions

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