Chapter 12, Problem 39RE

To determine

To find: The general form for the arithmetic sequence.

Answer to Problem 39RE

The general from of the sequence is,

  $a_n=n-10$

Explanation of Solution

Given:

The 10th term is $0$ and the 18th term is 8.

Calculation:

Consider the general term of the arithmetic sequence is,

  $a_n=a_1+\left(n-1\right)d$

For 10th term is $0$ ,

  $\begin{array}{l}0=a_1+\left(10-1\right)d\\ 0=a_1+9d\end{array}$ ..........(I)

For the 18th term is 8,

  $\begin{array}{l}8=a_1+\left(18-1\right)d\\ 8=a_1+17d\end{array}$

From equation (I) and from above,

  $d=1$

Then,

  $\begin{array}{l}0=a_1+9\left(1\right)\\ a_1=-9\end{array}$

Then, the general form of the sequence is,

  $\begin{array}{c}{a}_n=-9+\left(n-1\right)\left(1\right)\\ =n-10\end{array}$