Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively

Answer 1

if you divide 5th term with 2ed you'll get cube of the common ratio.
once you get the common ratio then square it and divide 2ed term which is -36 you'll get the scale factor.

Answer 2

Could you walk me through it? This makes no sense to me

Answer 3

ok.
see this is GP
\[a,\ ar,\ ar^2,\ ar^3,\ ar^4,\ \ldots\]
second term is \[ar\]=-36
fifth term is \[a*r^4=\] 2304
fifth term divided with second term
ar^4/ar =r^3={2304/(-36)}=-64
r=-4
now divide second term which is ar=-36 with r
ar/r = a =-36/(-4) = 9
a=9
so nth term is
\[a*r^{n-1}\]
where a is 9 and r is -4

Answer 4

an = so 9 x 4^(n-1)

Answer 5

its -4 not 4

Answer 6

Than you so much!!