Q:

Which number best completes the sequence: 2, 9, 5, 13, 10, 19 and 17?

A:

The number 17 best continues the following sequence: 2, 9, 5, 13, 10, 19. A sequence, in math terms, is a set of numbers organized in some sort of pattern. To find the next number in the sequence, the problem's solver must first figure out the pattern.

The differences between the numbers are 7, -4, 8, -3 and 9. The numbers switch on and off from adding or subtracting. Every time a number is added, it is one higher than the last number that was added. In the pattern so far, the positive numbers are 7, 8, and 9. Every time a number is subtracted, it is one less than the last subtraction. The negative numbers so far are -4, and -3. Using this pattern, the next number is 2 less than the last number in the sequence, 19. So, the answer is 17.

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