Question

In a geometric sequence, a^11=72 and a^13=1/2. use the geometric mean to find the value of a^12

Answer 1

If a, b, c is a geometric sequence, then
`ac=b^2`

We have:

`a_(11)=72;\ a_(12);\ a_(13)=(1)/(2)`

substitute:

`(a_(12))^2=72\cdot(1)/(2)\\\\(a_(12))^2=36\to a_(12)=\pm√(36)\\\\a_(12)=-6\ \vee\ a_(12)=6`