Multiple choice

The sum of first $15$ terms of the series $1, 3,5, ........$ is

  1. $225$
  2. $150$
  3. $200$
  4. $250$
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A Correct answer
Explanation

The series is 1, 3, 5... which is an arithmetic progression with a=1, d=2. Sum of n terms = n^2. For n=15, sum = 15^2 = 225.

AI explanation

The series is an arithmetic progression with the first term a = 1 and the common difference d = 2. We use the sum formula for an arithmetic progression, S = n/2 [2a + (n - 1)d]. Substituting n = 15 gives S = 15/2 [2(1) + (15 - 1)2] = 15/2 [2 + 28] = 15 * 15 = 225.

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