Question

Find the indicated term in each arithmetic sequence.
$90$th term of$1,-2,-5,....$

Short answer

The solution is$-266$.

Step-by-step solution

Step 1. Given information 

Arithmetic sequence:$1,-2,-5,....$

Step 2. Calculation 

The first term of the arithmetic sequence is $a_1=1$, and the common difference is$d=-3$.

Now, the $90$th term is -

$a_n=a_1+\left(n-1\right)d$

role="math" localid="1648710639831" $a_{90}=1+\left(90-1\right)\left(-3\right)$

$=1+\left(-267\right)$

$=-266$