SOLUTION: 6250 + 1250 + 250 + ... +2

Question 1108530: 6250 + 1250 + 250 + ... +2
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we have a geometric series
:
x(n) = ar^(n-1) with a=6250 and r=(1/5)
:
2 = 6250(1/5)^(n-1)
:
(2/6250) = (1/5)^(n-1)
:
(1/3125) = (1/5)^(n-1)
:
n-1 = log (base 1/5) (1/3125)
:
n-1 = 5
:
n = 6
:
there are 6 terms to sum
:
Note 2 = 6250(1/5)^5 = 6250/3125 = 2
:
the sum of the first n terms in a geometric sequence is
:
S(n) = a(1 - r^n) / (1 - r)
:
for this problem n = 6 and r = 1/5
:
S(6) = 6250(1 - (1/5)^6) / (1 - (1/5))
:
S(6) = 6250(1 - 0.000064) / (1 - (1/5))
:
*****************************
S(6) = 6250 * 1.24992 = 7812
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:
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