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

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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To find the 7th term in a geometric sequence, we can use the geometric mean between the 6th and 8th terms.

The geometric mean is the square root of the product of two numbers. In this case, we'll use the 6th term (50) and the 8th term (18).

Step 1: Find the product of the 6th and 8th terms.
Product = 50 * 18 = 900

Step 2: Take the square root of the product.
Square root of 900 = 30

Therefore, the 7th term in the geometric sequence is 30.

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