If the sum of the three consecutive terms of A.P. is 48 and the product of the first and the last is 252, then d = _____

Question

Philoid · Accepted Answer

We know that the sum of 3 nos in the AP is 48.

Lets say that those 3 nos are : a – d, a, a + d

So we can say that, a – d + a + a + d = 48

3a = 48

a= 16

now we have product of the first and the last term out of these 3 to be 252.

Ie. (a – d)(a + d) = 252

⇒ a² – d² = 252

we have a = 16, so we put the value of a in the above equation:

⇒ (16)² – d² = 252

⇒ 256 – d² = 252

⇒ d² = 256 – 252

⇒ d² = 4

⇒ d=2

∴ the correct option is (a)