Chapter 4.6, Problem 33E

To determine

To write: An equation for the $n\mathrm{th}$ term of the arithmetic sequence. Then find $a_{10}$ .

Answer to Problem 33E

  $a_n=-6+n$

  $a_{10}=4$

Explanation of Solution

Given information: Given sequence is $-5,-4,-3,-2,\mathrm{.....}$ .

Calculation: Given sequence is $-5,-4,-3,-2,\mathrm{.....}$ .

Common difference $=a_2-a_1=-4+5=1$ .

  $n\mathrm{th}$ Term of arithmetic sequence is $a_n=a+(n-1)d$

Here $a=-5\mathrm{and}d=1$ put this value in $a_n$

  $\begin{array}{l}{a}_n=a+(n-1)d\\ a_n=-5+(n-1)1\\ a_n=-5+n-1\\ a_n=-6+n\end{array}$

Here $n=10$ put this value in $a_n$ .

  $\begin{array}{l}{a}_{10}=-6+n\\ a_{10}=-6+10=4\end{array}$

Therefore $a_{10}=4$ .