find the first four terms of a sequence of which sum to n terms is 1/2 n (7n-1)

Answer :

Given : Sum to n terms is $\frac{1}{2}n\left(7n - 1\right)$ , So 

For n  = 1 , we get first term , So

First term  =  $\frac{1}{2}1\left(7\times 1 - 1\right) = \frac{1}{2}\times 6 = \mathbf{3}$

For n  = 2 , we get Sum of first two terms , So

Sum of first two terms  =  $\frac{1}{2}\times 2\left(7\times 2 - 1\right) = 14- 1 = \mathbf{13}$

Then Second term  =  13 -  3  =  10 

And

For n  = 3 , we get Sum of first three terms , So

Sum of first three terms  =  $\frac{1}{2}\times 3\left(7\times 3 - 1\right) = \frac{1}{2}\times 3\times 20 = \mathbf{30}$

Then Third term  =  30 -  13  =  17

And

For n  = 4 , we get Sum of first four terms , So

Sum of first four terms  =  $\frac{1}{2}\times 4\left(7\times 4 - 1\right) = 2\times 27 = \mathbf{54}$

Then fourth term  = 54 -  30  =  24

Then

First four terms of sequence  =  3 , 10  , 17 , 24                             (  Ans )