Question

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.

Answer 1

$The\ geometric\ mean\ of\ x\ and\ y:a=\sqrt{xy}\\\\a_6=50;\ a_8=18;\ a_7=?\\\\a_7=\sqrt{a_6\cdot a_8}\\\\subtitute\\\\a_7=\sqrt{50\cdot18}=\sqrt{900}=30\\\\Answer:\boxed{a_7=30}$

Answer 2

The geometric mean of two numbers, a and b = √ab 

Therefore the geometric mean of 50 and 18 = √(50 * 18) = √900 

And √900 = 30. 

Therefore the 7th term = 30