Answer
$a_{90} =-266$
Work Step by Step
The $n^{th}$ term of an arithmetic sequence is given by the formula:
$a_n = a_1 + (n-1)d (1)$
where
$a_1 = \ First \ Term; \\ d = \ Common \ Difference$
We have: $a_1=1 \\ d=a_2-a_1=-2-1=-3$
We will substitute the above data into formula (1) to obtain:
$a_n=1+(-3) (n-1) \implies a_n=1-3(n-1)$
In order to compute the $90th$ term, we need to plug in $90$ for $n$ into the above form to obtain:
$a_{90} = 1-3(90-1)=1-(89)(3)$
So, $a_{90} =-266$
