Question

What is the common ratio of the infinite geometric series with a1 = 24 and S = 48?

a) 0.5
b) 1
c) 2
d) 3

Answer 1

Using the formula for the sum of an infinite geometric series, the common ratio for a series with a first term of 24 and a sum to infinity of 48 is found to be 0.5.

Step-by-step explanation:

The question asks for the common ratio of an infinite geometric series where the first term (a1) is 24 and the sum to infinity (S) is 48. To find the common ratio (r), we use the formula for the sum of an infinite geometric series: S = a1 / (1 - r), where S is the sum to infinity, a1 is the first term, and r is the common ratio.

Since we know that S = 48 and a1 = 24, we can substitute these values into the formula to find r:

48 = 24 / (1 - r)

2 = 1 / (1 - r)

2 - 2r = 1

1 = 2r

r = 1 / 2

Therefore, the common ratio of the infinite geometric series is 0.5.