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

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 

S51 = 3774

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