Question

If 7 times of the 7^th term of an AP is equal to 11 times its 11th term then find the 18th term of the AP ?

Answer 1

Correct Answer - Option 1 : 0

CONCEPT:

Let us suppose a be the first term and d be the common difference of an AP. Then the nth term of an AP is given by: an = a + (n - 1) × d

CALCULATION:

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

Let the first term be a and d be the common difference of the AP

As we know that, if a is the first term and d is the common difference of an AP then an = a + (n - 1) × d

⇒ 7 × (a + 6d) = 11 × (a + 10d)

⇒ 7a + 42d = 11a + 110d

⇒ 4a = - 68d

⇒ a = - 17d

Here, we have to find the 18th term

⇒ a₁₈ = a + 17d = a - a = 0-----(∵ a = - 17d)

Hence, correct answer is 1.