Sequence

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.

a_n is the nth term.

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
a_n = n + 1.

So a_n = n + 1.

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
a_n = n².

So a_n = n².