Question

if the 10th term of an AP is 52 17 th term is 20 more than the 13 th term. find the AP

Answer 1

Let the first term and the common difference of the given A.P. be a and d respectively.

Then,

Second term (a ₂) = a + d

Fourth term (a ₄) = a + 3d

Eighth term (a ₈) = a + 7d

Given : a ₈ - a ₄ = 16

⇒ a + 7d - (a + 3d) = 16

⇒ a + 7d - a - 3d = 16

⇒ 4d = 16

⇒ d = 16/4 = 4

Also

a ₂ = 13

⇒ a + d = 13

⇒ a + 4 = 13

⇒ a = 13 - 4 = 9

Hence, the required A.P. is 9, 13, 17, 21, .....