Question

If $9^{\text {th }}, 13^{\text {th }}$ and $15^{\text {th }}$ terms of an arithmetical progression are the first three terms of a geometric series whose sum of infinite terms is 80 , then which of the following hold(s) good?

• A. Sum of the first 16 terms of the geometric progression is 860 .
• B. First term of the arithmetic progression is 80 .
• C. First term of the geometric progression is 40 .
• D. If $d$ is the common difference of arithmetic progression and $r$ is the common ratio of geometric progression then $dr =\frac{-5}{2}$.

Answer 1

Answer: (B), (C), (D)

Let a and d be the first term and common difference of arithmetic progression. Also, let $b$ and $r$ be the first term and common ratio of geometric progression