# 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*_{n} = *n* + 1

Inductive reasoning

## Example 2

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

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

## Example 3

Find the pattern between the terms.*a*_{1} = (-3)^{0}*a*_{2} = (-3)^{1}*a*_{3} = (-3)^{2}

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