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?

$a_1=5;d=-3$

Short answer

The $n$th term is localid="1648724564160" $a_n=8-3n$and the fifty-first term $-145$.

Step-by-step solution

Step 1. Given information

$a_1=5;d=-3$

Step 2. Calculation

The $n$thterm is -

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

localid="1648724489206" $=5+\left(n-1\right)\left(-3\right)$

$=5-3n+3$

$=8-3n$

and the fifty-first term is -

localid="1648664026002" $a_{51}=5+(51-1)\left(-3\right)$

$=5+\left(-150\right)$

$=-145$