# Find the indicated term of the geometric sequence. 5th term of {eq}1, -3, 9, ... {/eq}

## Question:

Find the indicated term of the geometric sequence.

5th term of {eq}1, -3, 9, ... {/eq}

## Geometric sequence:-

A geometric sequence is a pattern or arrangement of numbers. In this pattern, each term of the sequence is equal to the previous term by a coefficient constant.

This coefficient constant is defined as the common ratio {eq}r {/eq} of the geometric sequence.

A geometric sequence can be finite or infinite.

So a geometric sequence is given as below:-

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

Where {eq}a {/eq} is the first term and {eq}r {/eq} is the common ratio of the geometric sequence.

So $$\displaystyle r = \frac{ar}{a}= \frac{ar^2}{ar}= \frac{ar^3}{a^2}= \cdot\cdot\cdot$$.

The general term of the geometric sequence:-

The general term of the geometric sequence is given by the following formula:-

$$a_n = ar^{n-1}$$

Where {eq}n {/eq} is the number of the term in the geometric sequence.

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Given:-

$$1, -3, 9,\cdot\cdot\cdot$$ is a geometric sequence.

So $$r = \frac{-3}{1}= \frac{9}{-3}= -3$$

$$a = 1~ \text{and} ~n=5$$

So...