SOLUTION: What is the sum of the geometric series linked below? https://s31.postimg.org/upv8rqf7v/gseries.png A.) 198.4375 B.) 96.875 C.) 196.875 D.) 396.875

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Question 1041317: What is the sum of the geometric series linked below?
https://s31.postimg.org/upv8rqf7v/gseries.png
A.) 198.4375
B.) 96.875
C.) 196.875
D.) 396.875
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
solution is 196.875
you can use the sum of a geometric series formula, or you can just find A1 to A6 and add them up.

the formula for An is An = A1 * r^(n-1)
A1 = 100
r = 1/2

you get:
A1 = 100 * (1/2)^0 = 100 * 1 = 100
A2 = 100 * (1/2)^1 = 50 * 1/2 = 50
A3 = 100 * (1/2)^2 = 100 * 1/4 = 25
A4 = 100 * (1/2)^3 = 100 * 1/8 = 12.5
A5 = 100 * (1/2)^4 = 100 * 1/16 = 6.25
A6 = 100 * (1/2)^5 = 100 * 1/32 = 3.125

add them up and you get 196.875

the sum of a geometric series formula is Sn = (A1 * (1 - r^n)) / (1-r)
A1 = 100
r = 1/2
n = 6

formula becomes S6 = (100 * (1 - (1/2)^6) / (1-r)
simplify to get S6 = (100 * (1 - 1/64) / (1 - 1/2)
simplify further to get S6 = (100 * 63/64) / (1/2)
simplify further to get S6 = 100 * 63/64 * 2
simplify further to get S6 = 100 * 126/64
simplify further to get S6 = 196.875

you got the same answer two different ways.
it looks good.