Question 1161936
<br>
2, 1, -4, 7, -10, 13, -16<br>
The signs are alternating (except at the beginning).  To analyze the sequence, change the sign of every other term to make most of the terms positive:<br>
-2, 1, 4, 7, 10, 13, 16<br>
We see this is an arithmetic sequence with common difference 3 and first term -2.  That makes the formula for the n-th term<br>
t(n) = 3n-5<br>
To get the alternating signs, we can add a factor of (-1)^n or (-1)^(n+1).  If we add a factor of (-1)^n, then the signs of the odd-numbered terms change, because -1 to any odd power is -1.<br>
That gives us the desired sequence:<br>
2, 1, -4, 7, -10, 13, -16<br>
So the formula for the general term is<br>
t(n) = ((-1)^n)(3n-5)<br>