If the sum and product of the first three terms in an A . P . are 33 and 1155 , respectively, then a value of its 11 t h term is:

Step-by-step solution

Let, the first 3 terms of the A . P . are a - d ,   a ,   a + d ⇒ s u m = 3 a = 33 ⇒ a = 11 And product a - d   a   a + d = a a 2 - d 2 = 1155 ⇒ 11 11 2 - d 2 = 1155 ⇒ 121 - d 2 = 1155 11 = 105 ⇒ d 2 = 121 - 105 = 16 ⇒ d = ± 4 For a = 11 ,   d = 4 , the A . P . is 7 ,   11 ,   15 , … The n t h term of an A . P . , with first term A and common difference d is T n = A + n - 1 d So, T 11 = 7 + 10 × 4 = 47 For a = 11 ,   d = - 4