As 1/4 + x + 1/36 + 1/108 + ... is a geometric series, each of the terms has a common ratio with the previous term.

So (1/108) / (1/36) = (1/ 36) / x

=> x = (1/36)^2 / (1/108)

=> x = 108/36^2

**=> x = 1/12**

Given the geometric series :

1/4 + x + 1/36 + 1/108+ ....

We need to find the value of x.

Let (r) be the common difference between terms.

Then we know that:

x = 1/4 * r...........(1)

1/36 = x * r.............(2)

We will use the substitution method to solve.

From (1) we know that r = 4x.

==> We will substitute into (2).

==> 1/36 = x*(4x)

==> 1/36 = 4x^2

Now we will subtract by 4.

==> x^2 = 1/144

Now we will take the square toot of both sides.

**==> x = 1/12**