Question

find the first four terms of a sequence of which sum to n terms is½n (7n-1)

Answer 1

Given : Sum to n terms is 12n(7n − 1) , So 

For n  = 1 , we get first term , So

First term  =  121(7×1 − 1) = 12×6 =  3

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

Sum of first two terms  =  12×2(7×2 − 1) = 14− 1 =  13

Then Second term  =  13 -  3  =  10 

And

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

Sum of first three terms  =  12×3(7×3 − 1) = 12×3×20 =  30

Then Third term  =  30 -  13  =  17

And

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

Sum of first four terms  =  12×4(7×4 − 1) = 2×27 =  54

Then fourth term  = 54 -  30  =  24

Then

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