How to find the nth term of an Arithmetic Sequence? (original) (raw)

Last Updated : 21 Aug, 2025

Answer - Use the formula: **a n = a 1 + (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:

**Step 2: **Find the Common Difference:

**Step 3: Use the Formula:

**a n = a 1 + (n - 1)d

**Step 4: Substitute Values:

**Step 5: Simplify and Solve:

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,

**a 9 = 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

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.

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