Question

Consider an infinite geometric series with the first term and common ratio. If its sum is 4 and the second term is \( \frac{3}{4} \), then:

• A. \( a = \frac{4}{7}, r = \frac{3}{8} \)
• B. \( a = 3, r = \frac{1}{8} \)
• C. \( a = \frac{3}{4}, r = \frac{1}{2} \)
• D. \( a = \frac{7}{4}, r = \frac{3}{4} \)

Hint:

For geometric series, the sum formula \( S = \frac{a}{1 - r} \) can be used to find the first term when the sum and ratio are known.

Answer 1

The Correct Option is D

Step 1: Use geometric series sum formula. The sum of an infinite geometric series is given by \( S = \frac{a}{1 - r} \), where \( a \) is the first term and \( r \) is the common ratio. Given the sum and second term, we can solve for \( a \) and \( r \).
Step 2: Conclusion. Thus, the correct values are \( a = \frac{7}{4} \) and \( r = \frac{3}{4} \).