The sun of the first five terms of a geometric series is 186 and the sum of the first six terms is 378. if the fourth term is 48, determine a,r, t10, S10

Answer 1

The sun of the first five terms of a geometric series is 186 and the sum of the first six terms is 378. if the fourth term is 48, determine a,r, t10, S10

Answer 2

Since S6 = S5 + T6,
378 = 186 + T6
T6 = 192

T6 = T4*r^2
192 = 48r^2
r^2=4
r=2

T4 = ar^3
48 = 8a
a = 6

Sequence is thus

6, 12, 24, 48, 96, 192, ...

T10 = 6*2^9 = 3072
S10 = 6*(1023) = 6138