Question 1197256
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As the response from tutor @ikleyn says, the problem is nonsense; there is no way to know what the subsequent terms of the sequence are.  ANY following numbers make a valid sequence.<br>
Tutor @MathLover1 assumes the sequence is quadratic and obtains a solution.  It is true that, given a sequence of 3 terms, there is a unique polynomial function of degree 2 for which f(1), f(2), and f(3) are the three given numbers.<br>
But the problem does not say that the sequence is quadratic; it is bad mathematics to assume it is.  Furthermore, there are an infinite number of polynomials of degree greater than 2 which produce the given first three numbers.<br>
A third "obvious" pattern is that the sequence of differences "plus 3, minus 7" repeats, giving the sequence<br>
-37, -34, -41, -38, -45, -42, -49, -46, -53, -50<br>
In that sequence, the "obvious" 10th term is -50.<br>
So go with the answer from tutor @ikleyn: The problem as posed is nonsense.<br>