Sequence

How to find the nth term of the given sequence by finding its pattern: 2 examples and their solutions.

Definition

Definition

A sequence is a set of numbers in order.

a1 is the first term.
a2 is the second term.
a3 is the third term.
a4 is the fourth term.

an is the nth term.

Example 1

Example

Solution

Find a pattern from the given terms.

Inductive Reasoning

The first term, a1, is 2.

2 = 1 + 1

So a1 = 1 + 1.

The second term, a2, is 3.

3 = 2 + 1

So a2 = 2 + 1.

The third term, a3, is 4.

4 = 3 + 1

So a3 = 3 + 1.

The fourth term, a4, is 5.

5 = 4 + 1

So a4 = 4 + 1.

The fifth term, a5, is 6.

6 = 5 + 1

So a5 = 5 + 1.

a1 = 1 + 1
a2 = 2 + 1
a3 = 3 + 1
a4 = 4 + 1
a5 = 5 + 1

Then
an = n + 1.

So an = n + 1.

Example 2

Example

Solution

Find a pattern from the given terms.

The first term, a1, is 1.

1 = 12

So a1 = 12.

The second term, a2, is 4.

4 = 22

So a2 = 22.

The third term, a3, is 9.

9 = 32

So a3 = 32.

The fourth term, a4, is 16.

16 = 42

So a4 = 42.

The fifth term, a5, is 25.

25 = 52

So a5 = 52.

a1 = 12
a2 = 22
a3 = 32
a4 = 42
a5 = 52

Then
an = n2.

So an = n2.