Multiple choice

If unity is added to the sum of any number of terms of the A.P 3 , 5 , 7 , 9............the resulting sum is

  1. a perfect cube

  2. a perfect square

  3. a number

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For AP 3, 5, 7, 9, ...: first term a=3, common difference d=2. Sum of n terms S_n = n/2[2a + (n-1)d] = n/2[6 + 2n - 2] = n(n+2). Therefore S_n + 1 = n² + 2n + 1 = (n+1)², which is a perfect square.

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