# math

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A geometric series has first term 8 and third term 20 what does the fifth term equal? What does the third partial sum equal?

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8 8r 8r^2

so 8 r^2 = 20
r^2 = 20/8 = 5/2
r = (5/2)^.5

so
8 8(5/2)^.5 8(5/2) 8(5/2)^1.5 8(5/2)^2
fifth term = 8(25/4) = 50

Sn = 8(1-r^n)/(1-r)
S3 = 8 (1-(2.5)^1.5)/(1 -2.5^.5)
40.65

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