Chapter 4.6, Problem 37E

To determine

To calculate: To write an equation for the nth term of the arithmetic sequence and then find $a_{10}$

Answer to Problem 37E

Nth term of arithmetic sequence is $a_n=20-10n$ and $a_{10}=-80$

Explanation of Solution

Given: Arithmetic sequence is $10,0,-10,-20,\mathrm{...}$

Formula Used:

Nth term of arithmetic sequence is given as

  $T_n=a+\left(n-1\right)d$ , where

  $a=$ First term

  $d=$ Common difference

Calculation:

Arithmetic sequence is given as follows:

  $10,0,-10,-20,\mathrm{...}$

Here, first term and common difference is

  $\begin{array}{l}a=10\\ d=0-10=-10\end{array}$

Nth term of sequence is given as follows:

  $\begin{array}{l}{a}_n=a+\left(n-1\right)d\\ a_n=10+\left(n-1\right)\left(-10\right)\\ a_n=10-10n+10\\ a_n=20-10n\end{array}$

  $a_{10}$ is calculated as follows:

  $\begin{array}{l}{a}_{10}=20-10\left(10\right)\\ a_{10}=20-100\\ a_{10}=-80\end{array}$

Conclusion:

Hence, Nth term of arithmetic sequence is $a_n=20-10n$ and $a_{10}=-80$