Multiple choice

What is the 15th term of the sequence 1, 7, 14, 22, 31,...?

  1. 148

  2. 176

  3. 250

  4. 351
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B Correct answer
Explanation

The sequence is 1, 7, 14, 22, 31. The differences are 6, 7, 8, 9. This is a quadratic sequence where the second difference is constant (1). The nth term is given by 0.5n^2 + 4.5n - 4. For n=15, 0.5(225) + 4.5(15) - 4 = 112.5 + 67.5 - 4 = 176.

AI explanation

The differences between consecutive terms increase by 1, as seen in the changes of 6, 7, 8, and 9, making the general formula n squared plus n all divided by 2, minus 1. For the 15th term, substitute 15 into the formula to get (15 squared plus 15) divided by 2, minus 1. This evaluates to (225 plus 15) divided by 2, minus 1, which equals 120 minus 1, resulting in 176.

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