Question

If 4 times the 4^th term of an A.P. is equal to 18 times its 18^th term, then find its 22^nd term.

Answer 1

Let a be the first term and d be the common difference of the A.P.

Then, 4 × a₄ = 18 × a₁₈   ...(Given)

⇒ 4(a + 3d) = 18(a + 17d)   ...[∵ a_n = a + (n – 1)d]

⇒ 2(a + 3d) = 9(a + 17d)

⇒ 2a + 6d = 9a + 153d

⇒ 7a = –147d

⇒ a = –21d

⇒ a + 21d = 0

⇒ a + (22 – 1)d = 0

⇒ a₂₂ = 0

Hence, the 22^nd term of the A.P. is 0.