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?

$a_1=-2;d=4$

Short answer

The $n$th term is localid="1648724438610" $a_n=4n-6$and the fifty-first term is$198$.

Step-by-step solution

Step 1. Given information

$a_1=-2;d=4$

Step 2. Calculation

The $n$th term is -

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

localid="1648724356281" $=-2+\left(n-1\right)4$

$=-2+4n-4$

$=4n-6$

and the fifty-first term is -

$a_{51}=-2+(51-1)4$

$=-2+200$

$=198$