Sequences

Sequences

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

Example 1

For the given sequence, find an. 2, 3, 4, 5, 6, ...

Find the pattern between the terms.

a1 = 1 + 1
a2 = 2 + 1
a3 = 3 + 1
...
an = n + 1

Inductive reasoning

Example 2

For the given sequence, find an. 1, 4, 9, 16, 25, ...

Find the pattern between the terms.

a1 = 12
a2 = 22
a3 = 32
...
an = n2

Example 3

For the given sequence, find an. 1, -3, 9, -27, 81, ...

Find the pattern between the terms.

a1 = (-3)0
a2 = (-3)1
a3 = (-3)2
...
an = (-3)n - 1