Sequence
How to find the nth term of the given sequence by finding its pattern: 2 examples and their solutions.
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.
Example2, 3, 4, 5, 6, ..., an = ?
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.
Example1, 4, 9, 16, 25, ..., an = ?
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.