Mathematics 2012 JAMB Past Questions - Question 20: The sum to infinity of a geometric progression is -1/10 and the first term is -1/8.Find the common ratio of the progression.

Correct Answer

B

Explanation

To find the common ratio (r) of a geometric progression when the sum to infinity is -1/10 and the first term is -1/8, we can use the formula for the sum of an infinite geometric series.The formula for the sum of an infinite geometric series is:S = a / (1 - r)Where S is the sum to infinity, a is the first term, and r is the common ratio.Given that S = -1/10 and a = -1/8, we can substitute these values into the formula:-1/10 = (-1/8) / (1 - r)To simplify the equation, we can multiply both sides by (1 - r):(-1/10)(1 - r) = -1/8Expanding the left side:-1/10 + (1/10)r = -1/8To eliminate the fractions, we can multiply both sides by the least common denominator, which is 40:-4 + 4r = -5Now, let's solve for r:4r = -5 + 44r = -1Dividing both sides by 4:r = -1/4Therefore, the common ratio of the geometric progression is -1/4.