If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term.

Question

Philoid · Accepted Answer

Given: 4 × a₄ = 18 × a₁₈

To find : a₂₂

Consider 4 × a₄ = 18 × a₁₈

⇒ 4 [a + (4 - 1)d] = 18 [a + (18 - 1)d]

⇒ 4a + 12d = 18a + 306d

⇒ - 14 a = 294 d

⇒ a = - 21d ………………(1)

Now, a₂₂ = a + (22 - 1)d

⇒ a₂₂ = a + 21d

⇒ a₂₂ = - 21d + 21d (from equation 1)

⇒ a₂₂ = 0

∴ a₂₂ = 0