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JEE Advanced 2014 Mathematics question

MathematicsSequence and SeriesJEE Advanced 2014

Let a, b, c be positive integers such that is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of

is

Answer: 4

Solution

Let the common ratio be , a positive integer; then b = ar, c = ar². The condition gives , i.e. $a(r -

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Question ID VK-026294