Question

If six times of the 3^rd term is equal to the eight times of 7^th term in an A.P., then what will be the 19^th term?

Answer 1

Let a be the first term and d be the common difference.

Then, according to the question,

6a₃ = 8a₇

⇒ 6(a + 2d) = 8(a + 6d)

⇒ 6a + 12d = 8a + 48d

⇒ 6a – 8a = 48d – 12d

⇒ – 2a = 36d

⇒ a = – 18d

Now, a₁₉ = a + 18d = (– 18d) + 18d = 0

Hence, the 19^th term of the A.P. is 0.