Question

Find the sum of the first 51 terms of the A.P: whose second term is 2 and the fourth term is 8.

Answer 1

51 terms of an A.P whose `a_2 = 2` and `a_4 = 8`

Now 

`a_2 = a + d`

2 = a + d .....(1)

Also

a_4 = a + 3d

8 = a+ 3d  ....(2)

Substracting 1 from 2 we get

2d = 6

d = 3

Further substituting d = 3 in (1) we get

2 = a + 3

a = -1

Number of terms (n) = 51

First term for the given A.P. (a) = −1

So, using the formula we get,

`S_n = 51/2[2(-1) + (51 - 1)(3)]`

`= (51/2)[-2 +(50)(3)]`

`= (51/2)[-2 + 150]`

`= (51/2)[148]`

= 3774

Therefore the sum of first terms for given A.P. is 3774