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

Optima Learn · 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 Progression — Previous Year Question

CAT 2025

Quantitative

Progression

Hard

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