Question

What is the geometric mean between 1 and 16?

Answer 1

-4 is also a geometric mean

if we consider a(first element in series)=1 and r(common ratio)=-4 then the series would be

1,-4,16,-64,256,…..,a(-4)^(n-1 )

where n is nth term

from this -4 would be the geometric mean if we consider -4 as common ratio .

If we consider 4 as common ratio then geometric mean should be 4

so you should mention whether common ratio >0 or not (r>0 or not) .

[without ‘r’ value you can’t solve the question but in general most of the teachers will consider r>0.]

So, -4 won’t be geometric mean of 1 & 16

Answer 2

Answer:

4

Step-by-step explanation:

The geometric mean of 2 numbers a and b is $\sqrt{ab}$ , so

geometric mean of 1 and 16 is

$\sqrt{1(16)}$ = $\sqrt{16}$ = 4