Question

The ratio of 6th to the 2nd term of geometric sequence is 256. If the 3rd term of this sequence is32 determine first and fifth term

Answer 1

Did you mean
ar^5 : ar = 256 : 1 ?
if so, then
ar^5/(ar) = 256
r^4 = 256
r = ± 4

if r = 4, then ar^2 = 32
16a = 32
a = 2

if r = -4 , then
16a 32
a = 2

term(5) = ar^4 = 2(4)^4 = 512

the 2 sequences are either:
2, 8, 32, 128, 512, 2048, ....
or
2, -8, 32, -128, 512, -2048, ...
for either one term(1) = 2, and term(5) = 512

and for either one, the ratio of
term(6) : term(2) = 2048/8 or -2048/-8 = 256 in each case