Multiple choice

What is the next term to this series, 2, 3, 7, 16, 32, and 57...?

  1. 94

  2. 93

  3. 92

  4. 95
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B Correct answer
Explanation

The differences between consecutive terms are: 3-2=1, 7-3=4, 16-7=9, 32-16=16, 57-32=25. These are squares of consecutive integers (1^2, 2^2, 3^2, 4^2, 5^2). The next difference should be 6^2 = 36. Thus, 57 + 36 = 93.

AI explanation

Find the pattern by calculating the differences between consecutive terms. The first differences are 1, 4, 9, 16, and 25, which represent the perfect squares of 1, 2, 3, 4, and 5. Following this sequence of squared differences, the next difference must be 6^2, which is 36. Add 36 to the last given term, 57, to obtain the next term, 93.

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