Question

Find the fierms of a sequence of which sum to n terms is 1/2n(7n-1)

Answer 1

Given : Sum to n terms is 12n7n - 1 , So 

For n  = 1 , we get first term , So

First term  =  1217×1 - 1 = 12×6 =  3

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

Sum of first two terms  =  12×27×2 - 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  =  12×37×3 - 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  =  12×47×4 - 1 = 2×27 =  54

Then fourth term  = 54 -  30  =  24

Then

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