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:

$a_{11}=72;\ a_{12};\ a_{13}=\dfrac{1}{2}$

substitute:

$(a_{12})^2=72\cdot\dfrac{1}{2}\\\\(a_{12})^2=36\to a_{12}=\pm\sqrt{36}\\\\a_{12}=-6\ \vee\ a_{12}=6$