Question

find the 21st term of the ap whose 7th term is 14 and 14th term is 21​

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,

7th term(T7) = 11th term (T11) - 24 [∵ nth term of an AP, Tn = a+(n-1)d]

⇒ a+(7-1)d = a+(11-1)d-24

⇒ a + 6d = a + 10d - 24

⇒ 24 = 4d ⇒ d = 6

∴ 20th term of AP, T20 = a+(20-1)d

= 12 + 19 × 6 = 126

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

hope it helps you