# Sequences

How to find the *n*th term of a given sequence by finding its pattern: examples and their solutions.

## Example 1

Find the pattern between the terms.*a*_{1} = 1 + 1*a*_{2} = 2 + 1*a*_{3} = 3 + 1*a*_{4} = 4 + 1*a*_{5} = 5 + 1

...

So *a*_{n} = *n* + 1.

## Example 2

Find the pattern between the terms.*a*_{1} = 1^{2}*a*_{2} = 2^{2}*a*_{3} = 3^{2}*a*_{4} = 4^{2}*a*_{5} = 5^{2}

...

So *a*_{n} = *n*^{2}.

## Example 3

Find the pattern between the terms.*a*_{1} = 1

= (-3)^{0}

Zero exponent*a*_{2} = (-3)^{1}*a*_{3} = (-3)^{2}*a*_{4} = (-3)^{3}*a*_{5} = (-3)^{4}

...

So *a*_{n} = (-3)^{n - 1}.