Question

Find the sum of 51 terms of the A.P. whose second term is 2 and the 4th term is 8.

Answer 1

Given: a₂ = 2 and a₄ = 8 and n = 51

We know that,

a₂ = a + d = 2 …(i)

and a₄ = a + 3d = 8 …(ii)

Solving the linear equations (i) and (ii), we get

a + d – a – 3d = 2 – 8

⇒ -2d = -6

⇒ d = 3

Putting the value of d in eq. (i), we get

a + 3 = 2

⇒ a = 2 – 3 = -1

Now, we have to find the sum of first 51 terms.

⇒ S₅₁ = 51 [-1 + 25 × (3)]

⇒ S₅₁ = 51 [74]

⇒ S₅₁ = 3774