Find a general term in simplest form for the sequence: $$2, 1, -4, 7, -10, 13, -16$$
This is what I tried:
$a_n = a_1 + (n - 1)\cdot d$
$a_n = 2 + (n-1)\cdot 3$
$a_n = (-1)^n (2+(n-1)\cdot 3)$
which doesn't work.
I am pretty confused regarding the first two terms of the sequence and how to deal with the lack of a negative number (all of the terms after that seem to follow a pattern of +,-,+,- so I think multiplying by $(-1)^n$ would help there), as well as the different change in value from the first to the second term in the sequence, where as all the following numbers seem to follow a more recognizable pattern to me.
Any help would be greatly appreciated.