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Find a formula for the nth term of the geometric sequence. Then find the indicated term of the...

Question:

Find a formula for the {eq}n {/eq}th term of the geometric sequence. Then find the indicated term of the geometric sequence.

9th term: 7, 21, 63, ...

Geometric Sequence:


The form {eq}a,a{r^2},a{r^3}, \ldots ,a{r^{n - 1}}, \ldots {/eq} represents the geometric progression sequence. Also, known as the infinite sequence. In finite series form, represented as {eq}a,a{r^2},a{r^3}, \ldots ,a{r^{n - 1}} {/eq}. Adding all the terms gives the general form {eq}{S_n} = \dfrac{{a\left( {1 - {r^n}} \right)}}{{1 - r}} {/eq}, or {eq}{S_n} = \dfrac{{a\left( {{r^n} - 1} \right)}}{{r - 1}} {/eq}.


Answer and Explanation: 1

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Given:


  • The geometric sequence is {eq}7,21,63, \ldots {/eq}.


The objective is to find the formula for the {eq}{n^{{\rm{th}}}} {/eq} term of...

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Geometric Sequence: Formula & Examples

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Chapter 27 / Lesson 26
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Learn about geometric sequences. Understand what a geometric sequence is, learn how to find the common ratio of a geometric sequence, and see examples.


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