Answer
$a_{90} = -266$
Work Step by Step
RECALL:
(1) The $n^{th}$ term of an arithmetic sequence can be found using the formula:
$a_n = a_1 + (n-1)d$
where $a_1$ = first term and $d$ = common difference
(2) The common difference $d$ can be found by subtracting any term to the next term of the sequence:
$d=a_n - a_{n-1}$
The given sequence has:
$a_1=1$;
$d=-2-1=-3$
Substitute these values into the formula for the $n^{th}$ term, we obtain:
$a_n=a_1 + (n-1)d
\\a_n=1+(n-1)(-3)
\\a_n=1+(-3)(n-1)
\\a_n=1-3(n-1)$
To find the 90th term, substitute $90$ for $n$ to obtain:
$a_{90} = 1-3(90-1)
\\a_{90}=1-3(89)
\\a_{90}=1-267
\\a_{90} = -266$