Question

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

A. 7  B. 11 C. 18 D. 0

Answer 1

D. 0

Let a and d be first term and common difference respectively

According to the question,

7 times the 7th term of an AP is equal to 11 times its 11th term

⇒ 7a_{7 =} 11a₁₁

As we know, nth term of an AP is

a_{n =} a + (n - 1)d

where a = first term

a_n is nth term

d is the common difference

we have,

7(a + 6d) = 11(a + 10d)

⇒ 7a + 42d = 11a + 110d

⇒ 4a + 68d = 0

⇒ a + 17d = 0

⇒ a_{18 =} 0

18th term of AP is 0