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.

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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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