Question

Evaluate the geometric series described.

-1 - 4 - 16 - 64..., n = 7

Answer 1

Given

A GP series ----> - 1 - 4 - 16 - 64 ......... + nth

n ----> number of terms

r ---> Common ratio = 2nd term / 1st term = - 4 / ( - 1 ) = 4

Sn = a*( r^n - 1 ) / ( r - 1 )

Sn = ( - 1 )*( 4^n - 1 ) / ( 4 - 1 )

here , n = 7

Sn = ( - 1 )*( 4^7 - 1 ) / ( 4 - 1 )

Sn = - 5461

Sum of the series ---> - 5461

nth = a*r^( n - 1 )

nth is the last term

nth = ( - 1 )*4^( 7 - 1 )

nth = ( - 1 )*4^6

nth = - 4096  

So, the GP series is - 1 - 4 - 16 - 64 ......... - 4096