Chapter 12.2, Problem 10E

To determine

Calculate the nth term and the $10th$ term of the arithmetic sequence.

Answer to Problem 10E

The arithmetic sequence is $a_n=3n-9$ and the $10th$ term is $21$ .

Explanation of Solution

Given:

It is given in the question that $a=-6,d=3$ .where first term a and common difference d .

Concept Used:

In this, use the concept of putting the value in the formula $a_n=a_1+(n-1)d$ and get the answer.

Calculation: Here, $a=-6,d=3$ ,

Using the sequence $a_n=a_1+(n-1)d$ ,

  $\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_n=-6+(n-1)(3)\\ a_n=-6+3n-3\\ a_n=3n-9\end{array}$

Now, by using the above sequence , put $n=10$

  $\begin{array}{l}{a}_n=3n-9\\ a_{10}=3(10)-9\\ a_{10}=30-9=21\end{array}$

Conclusion:

The arithmetic sequence is $a_n=3n-9$ and the $10th$ is $21$ .