SOLUTION: Find the sum of the first 10 terms of geometric series starting at 10 and decreasing by a factor of 2 each time? A 5 - 5/2^8 B 10 - 5/2^8 C 15 - 5/2^8 D 20

SOLUTION: Find the sum of the first 10 terms of geometric series starting at 10 and decreasing by a factor of 2 each time? A 5 - 5/2^8 B 10 - 5/2^8 C 15 - 5/2^8 D 20 - 5/2^8

Question 1022028: Find the sum of the first 10 terms of geometric series starting at 10 and decreasing by a factor of 2 each time?
A 5 - 5/2^8
B 10 - 5/2^8
C 15 - 5/2^8
D 20 - 5/2^8
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
the sum of a geometric series is Sn = a(1 - r^n) / (1 - r) where a is the first term, r is the common ratio, and n is n consecutive terms
:
S10 = 10(1 - (1/2)^10) / ( 1 - (1/2))
:
S10 = 10(1 - (1/(2^10))) / (1/2)
:
divide by 1/2 means multiply by 2
S10 = 20(1 - (1 /2^10)
:
20 = 2^2 * 5
S10 = 20 - (((2^2)*5)/ 2^10)
:
S10 = 20 - (5 / 2^8)
:
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Answer is D
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