Question

If 7 times the 7^th term of an AP is equal to 11 times its 11^th term, then its 18^th term will be ______.

विकल्प

• 7

• 11

• 18

• 0

Answer 1

If 7 times the 7^th term of an AP is equal to 11 times its 11^th term, then its 18^th term will be 0.

Explanation:

According to the question,

7a₇ = 11a₁₁

⇒ 7[a + (7 – 1)d] = 11[a + (11 – 1)d]    ...[∵ a_n = a + (n – 1)d]

⇒ 7(a + 6d) = 11(a + 10d)

⇒ 7a + 42d = 11a + 110d

⇒ 4a + 68d = 0

⇒ 2(2a + 34d) = 0

⇒ 2a + 34d = 0     ...[∵ 2 ≠ 0]

⇒ a + 17d = 0   ...(i)

∴ 18^th term of an AP,

a₁₈ = a + (18 – 1)d

= a + 17d   

= 0   ...[From equation (i)]