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Manipal MET2014MathematicsApplication of Derivatives

The largest term in the sequence a_n= n^2 n^3+200 is given by

Options

  1. A529 49
  2. B8 89
  3. C49 543
  4. DNone of these

Correct answer

C. 49 543

Step-by-step solution

Consider the function f(x)= x^2 x^3+200 aligned & & f^ (x) & =x (400-x^3 ) (x^3+200 )^2 =0 & & x^3 & =400 & & x & =(400)^ 1 / 3 aligned When x 0, f^ (x) 0x 0, f^ (x) 0 f(x) has maximum at x=(400)^ 1 / 3 Since, 7 (400)^ 1 / 3 8 , either a₇ or a₈ is the greatest term of the sequence. a₇= 49 543 , a₈= 8 89 and 49 543 8 89 a₇= 49 543 is the greatest.

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