Posted by PJ on .
The sum 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(first term),r(ratio), t10, S10.

Geometric series 
Reiny,
if sum(6) = 378 and sum(5) = 186
then term(6) = 378186 = 192
so
ar^5 = 192
ar^3 = 48
divide them
r^2 = 4
r = ±2
if r=2, then a(8) = 48 >a = 6
if r = 2, then a(8) = 48  a = 6
if a= 6, r=2, t(10) = 6(2^9) = 3072
if a= 6, r=2 , t(10) = 6(2)^9 = 3072
if a=6, r=2, sum(10) = 6(2^10  1)/1 = 6138
if a=6,r=2, sum(1) = 6((2)^10  1)/21) = 2046