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NDA 2016 Maths · Mathematics · Sequences and Series · hard

Three positive numbers in geometric progression have product 216 and sum 26. The greatest of them is

Single correct option

Three positive numbers in geometric progression have product 216216 and sum 2626. The greatest of them is
  1. A. 1212
  2. B. 1818
  3. C. 99
  4. D. 2424
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Answer: (B) 1818

Write the numbers as 6r,6,6r\dfrac6r,6,6r; the product is 63=2166^3=216, so the middle term is 6. The sum gives 6r+6r=20\dfrac6r+6r=20, i.e. 3r2−10r+3=03r^2-10r+3=0, so r=3r=3 or 13\tfrac13. The numbers are 2,6,182,6,18, and the greatest is 18. Choosing rr directly as 3 and reporting the ratio is a slip.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake