# arithmetic

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use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 50 and the 8th term is 18

• geometric sequence -

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• arithmetic -

by geometric mean

t7/t6 = t8/t7
t7^2 = (t6)(t8) = 18(50) = 900
so t7 = ± √900 = ±30

or

by definition
ar^5 = 50
ar^7=18
divide the 2nd by the first
r^2 = 18/50 = 9/25
r = ± 3/5
7th term = r x 6th term
= (3/5)(50) = 30 or (-3/5)(50) = -30

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