Question 165459: how do you do arithmetic and geometric series ?
Example
2 + 10 + 18 + 26 +...;find S10
3 + 15 + 75 + 375 + ...; find S 7
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! how do you do arithmetic and geometric series ?
Example
2 + 10 + 18 + 26 +...;find S(10)
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There is a common difference of 10-2 = 8 between each pair of terms, so:
d = 8; n=10, a(1) = 2
Formul:
S(n) = (n/2)(a+a(n)) where a(n) = a(1)+(n-1)d
a(10) = 2 + (10-1)*8 = 2 + 72 = 74
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S(10) = (10/2)(2+74) = 5*76 = 152
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3 + 15 + 75 + 375 + ...; find S(7)
There is a common ratio of 15/3 = 5 between each pair of terms, so:
r = 5; a(1) = 3
s(7) = 3[(5^7-1)/(5-1)] = 58,593
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Cheers,
Stan H.
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