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?

$a_1=2;d=3$

Short answer

The $n$th term is $a_n=3n-1$and the fifty-first term is$152$.

Step-by-step solution

Step 1. Given information 

$a_1=2;d=3$

Step 2. Calculation 

The $n$th term is -

$a_n=a_1+\left(n-1\right)d$

$=2+\left(n-1\right)3$

$=2+3n-3$

$=3n-1$

and the fifty-first term is -

$a_{51}=2+\left(51-1\right)3$

$=2+50·3$

$=152$