The sum of the first three terms of a geometric sequence is 49/ 32 and the sum of the next three terms is 49/ 256 . Find the common ratio and the first term of the sequence?
a(1-r^3)/(1-r) = 49/32
a(1-r^6)/(1-r) - 40/32 = 49/256
a(1-r^3)/(1-r) = 49/32
a(1-r^6)/(1-r) = 441/256
divide and you have
(1-r^3)/(1-r^6) = 8/9
solve for r (it's just a quadratic in r^3) and then you can find a.