Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 12 and the 8th term is 27. 20 19.5 18 17

A₆ = 12

a₇ = ? = x

a₈ 27

In this case x is the geometric mean & as per the formula

geometric mean of 2 numbers = √ (a₆ * a₈) = √ (12*27)

& x=18.

Proof:

Find the common ratio between a₇ & a₆ = = > = (x) / 12

now find the common ration between a₈ & a₇ = = = > = 27 / (x)

x/12 = 27/x = = = > x² = 12*27 = = > x² = 324 & x = √324 = 18