Posted by PJ on Sunday, January 6, 2013 at 9:28pm.
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, Sunday, January 6, 2013 at 11:03pm
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
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