Question

The terms of an infinitely decreasing geometric progression in which all the terms are positive, the first term is 4, and the difference between third and fifth term is \( \frac{32}{81} \), then which of the following is not true?

• A. \( S_{\infty} = 3 + 2\sqrt{2} \)
• B. \( r = \frac{1}{3} \)
• C. \( S_{\infty} = 6 \)
• D. \( r = \frac{2\sqrt{2}}{3} \)

Hint:

In a geometric progression, the sum of the infinite series is found using \( S_{\infty} = \frac{a}{1 - r} \) when \( |r| < 1 \).

Answer 1

The Correct Option is A