CAT 2025 Progression Question (Hard)

Question

Let a _ n be the n text th term of a decreasing infinite geometric progression. If a _ 1 a _ 2 a _ 3 52 and a _ 1 a _ 2 a _ 2 a _ 3 a _ 3 a _ 1 624 , then the sum of this geometric progression is

Accepted Answer

Let the first term be a and the common ratio be r. Given a a r a r 2 52 quad quad a 2 r a 2 r 2 a 2 r 3 624. From the first equation a 1 r r 2 52, so a 1 r r 2 . Substitute into the second 1 r r 2 2 r r 2 r 3 624 1 r r 2 13 3r 2-10r 3 0 3r-1 r-3 0 Simplify to get an equation in r its real solutions

CAT 2025

Quantitative

Progression

Hard

Let ( a _ { n } ) be the ( n ^ { \text {th } } ) term of a decreasing infinite geometric progression. If ( a _ { 1 } + a _ { 2 } + a _ { 3 } = 52 ) and ( a _ { 1 } a _ { 2 } + a _ { 2 } a _ { 3 } + a _ { 3 } a _ { 1 } = 624 ), then the sum of this geometric progression is

Build Interview Confidence in Days!

Resources

Features

Support