Question

Find the 20^th term of the AP whose 7^th term is 24 less than the 11^th term, first term being 12.

Answer 1

Let the first term, common difference and number of terms of an AP are a, d and n, respectively.

Given that,

First term (a) = 12

Now by condition,

7^th term (T₇) = 11^th term (T₁₁) – 24  ...[∵ n^th term of an AP, T_n = a + (n – 1)d]

⇒ a + (7 – 1)d = a + (11 – 1)d – 24

⇒ a + 6d = a + 10d – 24

⇒ 24 = 4d

⇒ d = 6

∴ 20^th term of AP,

T₂₀ = a + (20 – 1)d

= 12 + 19 × 6

= 126

Hence, the required 20^th term of an AP is 126.