CAT 2017 Progression Question (Hard)

Question

An infinite geometric progression a , a , a , has the property that a 3 a a for every n 1. If the sum a a a 32, then a is

Accepted Answer

Step 1 Let the first term be a and common ratio be r. Then , , , ... Sum of infinite GP Equation 1 Given The sum of terms from onward is a geometric series So Divide both sides by Solve Step 2 Substitute r 1 4 into Equation 1 a_5 a r 4 24 1 4 4 24 1 256 3 32a_5 is 3 32

CAT 2017

Quantitative

Progression

Hard

$An infinite geometric progression a₁, a₂, a₃,\dots has the property that aₙ = 3(aₙ₊₁ + aₙ₊₂ + \dots) for every n \geq 1. If the sum a₁ + a₂ + a₃ + \dots = 32, then a₅ is$

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