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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q. 26 (page 824)

Find the indicated term of each geometric sequence.
$8 t h$ term of $1, 3, 9, . . . . . .$

Short Answer

Expert verified

The $8 t h$ term is $2187$ .

Step by step solution

01

Step 1. Given information.

We have, $1, 3, 9, . . . . .$

$a_{1} = 1, a_{2} = 3, a_{3} = 9$

The common ratio is

$\frac{a_{2}}{a_{1}} = \frac{3}{1} = 3 \frac{a_{3}}{a_{2}} = \frac{9}{3} = 3$

Thus, the common ratio $r = 3$ .

02

To find the 8th term.

The $n t h$ term of a geometric sequence is determined by formula $a_{n} = a_{1} r^{n - 1}$

Substitute $a_{1} = 1, r = 3$ and $n = 8$

$a_{8} = 1 {(3)}^{8 - 1} a_{8} = 3^{7} a_{8} = 2187$

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Most popular questions from this chapter

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

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