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Question:
If $7^{\text {th }}$ and $13^{\text {th }}$ terms of an AP be 34 and 64 respectively then find its $18^{\text {th }}$ term.

Solution:

Given: $7^{\text {th }}$ term is 34 and $8^{\text {th }}$ term is 64

To find: find its $18^{\text {th }}$ term

34 = a + 6d ………….equation1

64 = a + 12d ………… equation2

Subtract equation1 from equation2 we get

d = 5

Put in equation1 we get

a = 4

So $18^{\text {th }}$ term is

4 + 17 × 5 = 89