Let us take terms of GP as $$a,ar,ar^2$$

then the terms in AP will be $$ar,ar^2,a$$

In that case, $$ar^2=\frac{(a+ar)}{2}$$

$$2ar^2=a+ar$$

On simplifying the equation, we get r =  or r = -1/2

r can not be 1 as that will make each term of the GP same which will not make it an infinite GP, so we get r = -1/2

⇒ Also given that sum to infinite terms of the GP = 36

$$\frac{a}{1-r\ }=36$$

plugging r=-1/2 we get

a = 54.