How to find the nth term of an Arithmetic Sequence?

Last Updated : 21 Aug, 2025

Answer - Use the formula: a_n = a₁ + (n - 1)d

Where:
a_n = nth term,
a = first term,
d = common difference,
n = term number.
Substitute the values of a, d, and n into the formula to calculate a_n.

Steps to find the n^th Term of an Arithmetic Sequence

Step 1: Identify the First and Second Term:

1st and 2nd term, that is a₁ and a₂.

Step 2:Find the Common Difference:

Subtract the first term from the second term (d = a₂- a₁)

Step 3: Use the Formula:

a_n = a₁ + (n - 1)d

Step 4: Substitute Values:

Plug in the values of a, d, and n into the formula.

Step 5: Simplify and Solve:

Perform the arithmetic operations to find the nth term.

Solved Problems - How to find the nth term of an Arithmetic Sequence?

Question 1: Find the 9th term of the given series, {1, 4, 7, 10, 13, 16,....}

Solution:

Term number (n) is 9,
1st-term, a₁ = 1
2nd term, a₂= 4,
Now find the common difference,
d = a₂ - a₁= 4 - 1 = 3
Now the 9th term,
a₉ = First term + (Last term - 1) × common difference
= a₁ + (n - 1)d
= 1 + (9 - 1) × 3
= 1 + 8 × 3
= 1 + 24
= 25
So, the 9th term is 25.

Question 2: Find the 7th term of an AP whose 3rd term is 9 and 5th term is 15?

Solution:

Given
3rd term (a₃) = 9
5th term (a₅ ) = 15
Here we have to find common difference and first term(a₁).
a₃ = a₁+ 2d = 9 [from the formula] ⇢ (1)
And, a₅= a₁+ 4d = 15 ⇢ (2)
Solve (1) and (2),
a₁+ 2d = 9 ⇢ (1)
a₁+ 4d = 15 ⇢ (2)
Let's apply subtraction between (1) and (2)
2d = 6, d=3
So, the common difference is 3
Now put the value of d in any one equation, here put the value of d in (1)
a₁+ 2d = 9
= a₁ + 2 × 3 = 9 [d = 3]
= a₁= 9 - 6
= a₁= 6
So the first term is 3
Now to find the 7th term,
Apply the formula for finding the nth term, here n = 7
a₇ = First term + (7th term - 1) × common difference
a₇ = a₁+ (7 - 1)d
a₇= 3 + 6 × 3 [d = 3 and a₁= 3]
a₇ = 21
So the 7th term is 21.