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NDA2016MathematicsDefinite IntegrationActual

Given that a _ n = ₀^ ^2 ( n +1) x 2 x dx Consider the following statements: 1. The sequence a_ 2 n is in AP with common difference zero. 2. The sequence a _ 2 n +1 is in AP with common difference zero. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

C. Both 1 and 2

Step-by-step solution

a_n= ₀^ ^2 (n+1) x 2 x d x Since it is a definite integral will have a definite value. The sequence a_ 2 n is in AP with common difference. Statement (1) is correct. The sequence a_ 2 n+1 is also in AP with common difference. Statement (2) is correct.

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