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AP EAMCET202021 Sep 2020Evening ShiftMathematicsSequences and SeriesActual

The sum of the cubes of three consecutive natural numbers is divisible by

Options

  1. A26
  2. B25
  3. C9
  4. D7

Correct answer

C. 9

Step-by-step solution

Let the three consecutive natural numbers ((n-1), n, n+1 ) where (n 2 ) ( ) Sum of cubes of the three consecutive natural numbers is ((n-1)^3+n^3+(n+1)^3=3 n^3+6 n=3 n (n^2+2 ) ) For each value of (n 2 ), the expression (3 n (n^2+2 ) ) is divisible by 9 . Hence, option (c) is correct.

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