Question

Identify the 12th term of a geometric sequence where a1 = 8 and a6 = −8,192.

Answer 1

−57,395,628

: )

Answer 2

geometric sequence

`a_(n)=a_(1)*r^(n-1)`
r=common ratio
a1=first term
find r

a1=8
a6=-8192

`-8192=a_(6)=8*r^(6-1)`

`-8192=8*r^(5)`
divide both sides by 8

`-1024=8*r^(5)`
take 5th root of both sides
-4=r
sub

`a_(12)=8*(-4)^(12-1)`

`a_(12)=8*(-4)^(11)`

`a_(12)=8*-4194304`

`a_(12)=-33554432`