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NDA 2 2024 Maths, question 13

Topic: Algebra

Q13

If the sum of the first nn terms of a series is n(2n+1)n(2n+1), then what is the nthnth term?

  1. (a) 4n−14n-1Correct answer
  2. (b) 4n4n
  3. (c) 4n+14n+1
  4. (d) 4n+34n+3

Solution.

Answer: (a) 4n−14n-1

  1. The nth term is Sₙ−Sₙ₋₁.
  2. Thus aₙ=(2n²+n)−[2(n−1)²+(n−1)]=4n−1.
  3. For n=1 this gives 3, agreeing with S₁.