It seems that the numbers go farther and farther from a central point, one at a time, so the sequence would be 1, 2, 0, 3, -1, 4, -2, 5, -3, 6, etc. (The terms in odd positions go down one at a time, the terms in even positions go up one at a time.)
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You cant solve the next term (next number) in this sequence. You need more terms, because this is either a "quadratic sequence", or a "linear and quadratic sequence", and you need more terms than this to solve a "linear and quadratic sequence" and for this particular "quadratic sequence" you would need more terms to solve nth term, which would solve what the next number is. If this is homework, check with your teacher if he wrote the wrong sum.
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16 is the next squared number.