Multiple choice

In the Number series given below, one number is missing. Series is followed by five alternatives. One of them is the right answer. Identify and indicate it as per the "Instructions". $2,35,104,209,....$

  1. $350$
  2. $248$
  3. $256$
  4. $311$
  5. $413$
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A Correct answer
Explanation

The pattern follows (n^3 + 1) where n starts at 1: (1^3+1)=2, (3^3+8)=35 (this is not a simple n^3+1). Looking at differences: 35-2=33, 104-35=69, 209-104=105. Second differences: 69-33=36, 105-69=36. The next difference is 105+36=141. 209+141=350.

AI explanation

The differences between the consecutive terms of the series are 33, 69, and 105. Examining these differences reveals a second level pattern where the differences of the differences are 36 (which is 69 minus 33) and 36 (which is 105 minus 69). Since the second difference is constant, the next first difference will be 105 plus 36, which equals 141, making the next term of the series 350 (209 plus 141).

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