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Chapter 5: Problem 72

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{5}\), when \(a_{1}=4, r=3\).

Short Answer

Expert verified
The fifth term (\(a_{5}\)) of the geometric sequence is 324.

Step by step solution

01

Understanding Geometric Sequence

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. We have the first term, \(a_{1}=4\), and the common ratio, \(r=3\).
02

Formula for the nth Term of a Geometric Sequence

The formula to find the nth term of a geometric sequence is given by \(a_{n} = a_{1}(r)^{n-1}\). To find the fifth term (\(a_5\)), we should replace \(a_{1}\) by 4, \(r\) by 3, and \(n\) by 5 in the formula.
03

Substitution and Calculation

Substituting the given values into the formula, we have \(a_{5} = 4(3)^{5-1} = 4(81)= 324\).

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Most popular questions from this chapter

What is the common ratio in a geometric sequence?

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-1000, r=0.1\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(-9,-5,-1,3, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{8}\), when \(a_{1}=6, r=\frac{1}{2}\).

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\frac{2}{3}, 1, \frac{4}{3}, \frac{5}{3}, \ldots\)
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