The first three terms of a geometric sequence is 9, 3, 1. Use general term formula to find the...

Question:

The first three terms of a geometric sequence is {eq}9,\ 3,\ 1 {/eq}. Use general term formula to find the 9th term.

The general term of a Geometric Sequence

A geometric sequence is an array of numbers in which each term has the common multiple to the preceding terms. Or in simple words, it is a series of numbers in which the ratio of two successive numbers is always constant, and this constant is known as the common ratio (r).

The general terms of a geometric sequence:

$$\displaystyle a,ar,ar^{2} ,ar^{3} ,...............,ar^{n-1},............$$

Here {eq}a = \text{First term} {/eq}

{eq}r = \text{Common ratio} {/eq}

The nth term of a geometric sequence:

$$\displaystyle a_{n} = a.r^{n-1}$$

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Given:

The first three terms of the geometric sequence are:

$$\displaystyle 9,3,1,...$$

{eq}\text{First term}(a) = 9 {/eq}

{eq}\text{Common...