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) = 378-186 = 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)/-2-1) = 2046

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