Question

If 7 times the 7^th term of an A.P. is equal to 11 times its 11^th term, then the value of its 18^th term is ______.

Answer 1

If 7 times the 7^th term of an A.P. is equal to 11 times its 11^th term, then the value of its 18^th term is 0.

Explanation:

Let a be the first term and d the common difference.

Then T₇ = a + 6d and T₁₁ = a + 10d.

Given 7T₇ = 11T₁₁

⇒ 7(a + 6d) = 11(a + 10d)

⇒ 7a + 42d = 11a + 110d

⇒ a + 17d = 0

Thus T₁₈ = a + 17d = 0.