question\nfind the 99th term of the arithmetic sequence 2, -3, -8, ...

Explanation:

Step1: Identify first - term and common - difference

The first - term $a_1 = 2$, and the common - difference $d=-3 - 2=-5$.

Step2: Use the formula for the nth term of an arithmetic sequence

The formula for the $n$th term of an arithmetic sequence is $a_n=a_1+(n - 1)d$. Substitute $n = 99$, $a_1 = 2$, and $d=-5$ into the formula: $a_{99}=2+(99 - 1)\times(-5)$.

Step3: Simplify the expression

First, calculate $99 - 1 = 98$. Then, $98\times(-5)=-490$. Finally, $a_{99}=2-490=-488$.

Answer:

$-488$