Question

Find the $n$th term of the arithmetic sequence $\left\{a_n\right\}$whose initial term $a_1$and common difference $d$are given. What is the fifty-first term?

$a_1=6;d=-2$

Short answer

The$n$th term is localid="1648724671067" $a_n=8-2n$and the fifty-first term is$-94$.

Step-by-step solution

Step 1. Given information

$a_1=6;d=-2$

Step 2. Calculation

The $n$thterm is -

$a_n=a_1+(n-1)d$

localid="1648724608193" $=6+\left(n-1\right)\left(-2\right)$

$=6-2n+2$

$=8-2n$

and the fifty-first term is -

localid="1648664061766" $a_{51}=6+\left(51-1\right)\left(-2\right)$

$=6+\left(-100\right)$

$=-94$