Chapter 12.2, Problem 15AYU

In Problems 17-24, find the nth term of the arithmetic sequence $\left\{a_n\right\}$ whose initial term $a_1$ and common difference $d$ are given. What is the 51st term?

$a_1=2;d=3$

To determine

To 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 51st term?

$a_1=2$; $d=3$

Answer to Problem 15AYU

$a_n=3n-1$

$a_{51}=152$

Explanation of Solution

Given:

$a_1=2$; $d=3$

Formula used:

If first term $a_1$, and common difference $d$ are known then $n$th term of the sequence is

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

Calculation:

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

$=2+3n-3=3n-1$

$a_n=3n-1$

$a_{51}=3\left(51\right)-1=153-1=152$