Question

Please help me out with question 2

Answer 1

n = 8

the sum to n terms of a geometric sequence is

`S_(n)` =
`(a(1-r^(n )) )/(1-r)`

where a is the first term and r the common ratio

here a = 16 and r =
`(64)/(-32)` =
`(-32)/(16)` = - 2

`S_(n)` = ( 16( 1 - ( - 2 )^n )/1 - (- 2 )) = - 1360

`(16)/(3)` ( 1 - (- 2 )^n ) = - 1360

multiply both sides by
`(3)/(16)`

1 - (- 2 )^n = - 255

- (- 2 )^n = - 256

)-2)^n = 256

note that
`2^(8)` and
`(-2)^(8)` = 256

hence n = 8