8. An infinite geometric series has a first term of 12 and a limiting sum of 15 . What is the common ratio?

Step 1 ：Given that the first term (a) of an infinite geometric series is 12 and the limiting sum (S) is 15.

Step 2 ：We can use the formula for the sum of an infinite geometric series, which is \(S = \frac{a}{1 - r}\), where r is the common ratio.

Step 3 ：Rearrange this formula to solve for r: \(r = 1 - \frac{a}{S}\).

Step 4 ：Substitute the given values into the formula: \(r = 1 - \frac{12}{15}\).

Step 5 ：Simplify to find the value of r: \(r = 0.19999999999999996\).

Step 6 ：Final Answer: The common ratio is approximately \(\boxed{0.2}\).