Question

Please help me out with question 2

Answer 1

n = 8

the sum to n terms of a geometric sequence is

$S_{n}$ = $\frac{a(1-r^{n )} }{1-r}$

where a is the first term and r the common ratio

here a = 16 and r = $\frac{64}{-32}$ = $\frac{-32}{16}$ = - 2

$S_{n}$ = ( 16( 1 - ( - 2 )^n )/1 - (- 2 )) = - 1360

$\frac{16}{3}$ ( 1 - (- 2 )^n ) = - 1360

multiply both sides by $\frac{3}{16}$

1 - (- 2 )^n = - 255

- (- 2 )^n = - 256

)-2)^n = 256

note that $2^{8}$ and $(-2)^{8}$ = 256

hence n = 8