Chapter 12.2, Problem 18AYU

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?

$a_1=6;d=-2$

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?

$a_1=6$; $d=-2$

Answer to Problem 18AYU

$a_n=8-2n$

$a_{51}=-94$

Explanation of Solution

Given:

$a_1=6$; $d=-2$

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:

$a_n=6+\left(n-1\right)(-2)$

$=6-2n+2=8-2n$

$a_n=8-2n$

$a_{51}=8-2\left(51\right)=8-102=-94$