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AIEEE 2004

JEE Main 2004 Mathematics question on Sequences and Series

An infinite GP has first term xx and sum 55, then xx belongs to
  1. A.
    x<−10x < -10
  2. B.
    −10<x<0-10 < x < 0
  3. C.
    0<x<100 < x < 10
  4. D.
    x>10x > 10
Show answer and solution

Correct option: C

Solution

For an infinite GP to converge, the common ratio r must satisfy |r| < 1. Here r = (5-x)/5, so |(5-x)/5| < 1, giving |5-x| < 5, which means 0 < x < 10. Also, x ≠ 0 (first term can't be zero). Additionally, the sum formula S = x/(1-r) = 5 requires x ≠ 0, so the valid range is 0 < x < 10.

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