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=√(xy)\\\\a_6=50;\ a_8=18;\ a_7=?\\\\a_7=√(a_6\cdot a_8)\\\\subtitute\\\\a_7=√(50\cdot18)=√(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