A ball dropped from 36 m above the ground rebounds to 1/3rd of the height it falls from. If it continues to rebound in this manner, find the total distance the ball can cover?

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Official Explanation

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Total distance covered by ball

= 36 + 2*(1/3)*36+ 2*(1/3)^2*36+....= 2*36 + 2*(1/3)*36+ 2*(1/3)^2*36+....-36

i.e. Total Distance

= 2*[36 + (1/3)*36+ (1/3)^2*36+....]-36

This is a geometric progression with first term, a = 36 and common ratio, r = 1/3…

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What this question tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.