We are given that the sum of the terms in an infinite geometric series is 15, and the sum of their squares is X.
To find the first term, we can use the formula for the sum of an infinite geometric series.
The formula is:
Sum = a / (1 - r), where a is the first term and r is the common ratio.
We are given that the sum is 15, so we can write:
15 = a / (1 - r)
Multiplying both sides of the equation by (1 - r) to eliminate the fraction, we get:
15(1 - r) = a
Expanding the equation, we have:
15 - 15r = a
Given that the value of the first term, a, is 5, we can substitute it into the equation:
15 - 15r = 5
Subtracting 15 from both sides of the equation, we find:
-15r = -10
Dividing both sides of the equation by -15, we get:
r = 2/3
Now, we know the first term, a, is 5 and the common ratio, r, is 2/3. We can use these values to find the sum of the squares of the terms in the series, which is X.
The formula for the sum of the squares of an infinite geometric series is:
Sum of squares = a^2 / (1 - r^2)
Substituting the values of a and r into the formula, we have:
X = (5^2) / (1 - (2/3)^2)
Simplifying, we get:
X = 25 / (1 - 4/9)
X = 25 / (5/9)
Multiplying by the reciprocal, we find:
X = 25 * (9/5)
X = 45
The value of X is 45.
The answer is: 45
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The sum of the terms in an infinite geometric series is 15, and the sum of their squares is X.  Find the first term.
If we know the answer to the above question is 5, what is the value of unknown variable X?

### Answer:
