Posted by **Taylor White** on Thursday, March 17, 2011 at 12:35pm.

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 -
**Writeacher**, Thursday, March 17, 2011 at 12:50pm
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- arithmetic -
**Reiny**, Thursday, March 17, 2011 at 1:35pm
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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