Chapter 12.2, Problem 20AYU

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?

$a_1=1;d=-\frac{1}{3}$

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?

$a_1=1$; $d=-\frac{1}{3}$

Answer to Problem 20AYU

$a_n=\frac{4-n}{3}$

$a_{51}=-\frac{47}{3}$

Explanation of Solution

Given:

$a_1=1$; $d=-\frac{1}{3}$

Formula used:

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

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

Calculation:

$a_n=1+\left(n-1\right)\left(-\frac{1}{3}\right)$

$=1-\frac{1}{3}n+\frac{1}{3}=\frac{4-n}{3}$

$a_n=\frac{4-n}{3}$

$a_{51}=\frac{4-51}{3}=-\frac{47}{3}$