Question

The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals

(a) −3
(b) 4
(c) 5
(d) 2

Answer 1

​Since, 3y − 1, 3y + 5 and 5y + 1 are first three terms of an A.P.

Then, Second term − First term = Third term − Second term = d (common difference)
⇒ 3y + 5 − (3y − 1) = 5y + 1 − (3y + 5)
⇒ 3y + 5 − 3y + 1 = 5y + 1 − 3y − 5
⇒ 6 = 2y − 4
⇒ 2y = 6 + 4
⇒ 2y = 10
⇒ y = 5

Hence, the correct option is (c).