The sum of n terms of an arithmetic series is Sn = 2n² + 6n. Find the first term and the
common difference.

Answer :

Here we have : The sum of n terms of an arithmetic series is S_n = 2n² + 6n

So,

S₁ =  2 ( 1 )²  + 6 ( 1 ) =  2 + 6 =   8

And

S₂ =   2 ( 2 )²  + 6 ( 2 ) =  2( 4 ) + 12 =   8  + 12  =  20

And

S₃ =  2 ( 3 )²  + 6 ( 3 ) =  2( 9 ) + 18 =   18  + 18  =  36

So ,

First term  =  Sum of one term  =  S₁ =   8 

And

Second term  =  S₂ -  S₁ =  20 -  8   = 12

And

Third term = S₃ -  S₂ =  36 - 20 =  16  , So Our A.P. , As :

8 , 12 , 16  , ...

So,

Common difference  =  12  -   8  =  16   - 12   =   4 

So,

First term =  8
An
Common difference  =  4                                                                             ( Ans )