MathematicsThe sum of the first n terms of an AP is 3 n 2 2 + 5n 2 ⋅ What is its nth term and the 25th term?

The sum of the first n terms of an AP is 3 n 2 2 + 5n 2 What is its nth term and the 25th term?


  1. A
    n th  term of AP is (3n+2) and the 25th term is 77.
  2. B
    n th  term of AP is (3n+1) and the 25th term is 76.
  3. C
    n th  term of AP is (3n1) and the 25th term is 86.
  4. D
    n th  term of AP is (3n+1) and the 25th term is 75. 

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    Solution:

    Given:
    S n = 3 n 2 2 + 5n 2 -----(1)
    Put n=(n-1) in equation (1).
    S n1 = 3 (n1) 2 2 + 5(n1) 2
      S n1 = 3 n 2 2n+1 2 + 5(n1) 2 = 3 n 2 n2 2
     Therefore, the  n th  term of the AP, a n
      = S n S n 1 = 3 n 2 +5n 2 3 n 2 n2 2
      = 6n+2 2 =3n+1. (2)
    Put n = 25 in equation (2):
    a 25 =3×25+1 a 25 =75+1 =76
    Therefore n th term and 25th terms of AP are (3n+1) and 76 respectively.
    Hence, option (2) is correct.
     
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