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
a4 = 4 + 1
a5 = 5 + 1
...

So an = n + 1.

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
a4 = 42
a5 = 52
...

So an = n2.

Example 3

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

Find the pattern between the terms.

a1 = 1
= (-3)0

Zero exponent

a2 = (-3)1
a3 = (-3)2
a4 = (-3)3
a5 = (-3)4
...

So an = (-3)n - 1.