A Geometric progression X has a first term of 4a and its sixth term is 256. Another Geometric progression Y has a first term of 3a and its fifth term is 48. Find the:
(i) First term of X
(ii) Sum of the first four terms of X
for X:
a = 4a, term(6) = (4a)r^5 = 256
ar^5 = 64
for Y:
a = 3a , term(5) = (3a)R^4 = 48
aR^4 = 16
r^5/R^4 = 3
3R^4 = r^5
Youd did not state whether R and r are equal , so without that information, that's as far as you can get.
If R = r, then cleary r = 4
and (4a)(4^5) = 256
1024a = 256
a = 1/4
I will let you do ii)