Question

if the sixth term of a G.P. is -1/32 and ninth term is 1/256, then eleventh term is what ?

Answer 1

Sixth term = T6 = -1/32

ninth term = T9 = 1/256

then , common ratio = R = ?

11th term = T11 = ?
_______________

R^p-q = Tp/Tq

R^9-6 = (1/256)/-1/32

R^3 = 1/256 × -32

R^3 = 1/-8

R^3 = -1/8

R^3 = (-1/2)^3

R = -1/2 .
__________

T6 = a(R)^n-1

-1/32 = aR^6-1

-1/32 = aR^5

-1/32 = a × (-1/2)^5

-1/32 = a × -1/32

(-1/32)/(-1/32) = a

-1/32 × -32 = a

-1×-1 = a

1 = a

a = 1
________________

T11 = aR^n-1

T11 = (1)(-1/2)^11-1

T11 = (-1/2)^10

T11 = 1/1024
___________________

Answer 2

Answer:

if the sixth term of a G.P. is -1/32 and ninth term is 1/256, then eleventh term i