Which term of the AP 3, 8, 13, 18, ... will be 55 more than its 20th term?

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Solution

Here, a = 3 and d = (8 - 3) = 5
The 20^th term is given by
T₂₀ = a + (20 - 1)d = a + 19d = 3 + 19 ⨯ 5 = 98
∴ Required term = (98 + 55) = 153
Let this be the n^th term.
Then T_n = 153
⇒ 3 + (n - 1) ⨯ 5 = 153
⇒ 5n = 155
⇒ n = 31
Hence, the 31^st term will be 55 more than its 20^th term.

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