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?

$a_1=0;d=\mathrm{\pi }$

Short answer

The $n$th term is $a_n=\left(n-1\right)\mathrm{\pi }$and the fifty-first term is $50\mathrm{\pi }$.

Step-by-step solution

Step 1. Given information

$a_1=0;d=\mathrm{\pi }$

Step 2. Calculation

The$n$th term is -

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

$a_n=0+\left(n-1\right)\mathrm{\pi }$

$a_n=\left(n-1\right)\mathrm{\pi }$

and the fifty-first term is -

$a_{51}=0+\left(51-1\right)\mathrm{\pi }$

localid="1648664439241" $=0+\left(50\right)\mathrm{\pi }$

$=50\mathrm{\pi }$