Chapter 12, Problem 21RE

To determine

To find:The general formula for the given arithmetic sequence.

Answer to Problem 21RE

The general formula for the given arithmetic sequenceis $a_n=n-10$ .

Explanation of Solution

Given information:

The tenth and eighteenth terms are 0 and 8.

Calculation:

The $n^{th}$ term of arithmetic sequence is,

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

The tenth term is,

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

The eighteenth term is,

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

From above equation $d=1$ .

Substitute the value in above equation.

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

Substitute the values in Equation (1).

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