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?

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 =(-5/2).

Tardigrade Admin · Accepted Answer

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

Q. If $9^{th}, 1 3^{th}$ and $1 5^{th}$ 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?

Sum of the first 16 terms of the geometric progression is 860 .

First term of the arithmetic progression is 80 .

First term of the geometric progression is 40 .

If $d$ is the common difference of arithmetic progression and $r$ is the common ratio of geometric progression then $d r = \frac{- 5}{2}$ .

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

Q. If 9th ,13th and 15th 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?