Question

find the 97th term of the arithmetic sequence -5, -23, -41,...

Explanation:

Step1: Identify sequence parameters

First term $a_1 = -5$, common difference $d = -23 - (-5) = -18$

Step2: Use arithmetic term formula

The $n$-th term formula is $a_n = a_1 + (n-1)d$

Step3: Substitute n=97 into formula

$$\begin{align*} a_{97} &= -5 + (97-1)(-18)\\ &= -5 + 96\times(-18)\\ &= -5 - 1728 \end{align*}$$

Answer:

$-1733$