Question

Please help meFind the geometric mean for each pair ofnumbers. Write an equation and solve,showing ALL the work.9 and 16

Answer 1

`\begin{gathered} To\text{ calculate geometric mean of any two numbers} \\ \text{Let the geometric mean of numbers a and c be k} \\ \text{then the sequence is a , k, c} \\ \text{common ratio r = }(k)/(a) \\ \text{also, common ratio r can also be written as r = }(c)/(k) \\ \text{equating the two common ratios} \\ (k)/(a)=(c)/(k) \\ k^2=ac \\ k=\sqrt[]{ac} \\ \text{Hence the geometric mean of two numbers a and c is }\sqrt[]{ac} \end{gathered}`

Now , to find the geometric mean of 9 and 16

`\begin{gathered} a=9,\text{ c= 16} \\ \text{Geometric mean, k =}\sqrt[]{ac\text{ }} \\ =\sqrt[]{9\text{ x 16}} \\ =\sqrt[]{144} \\ =12 \end{gathered}`