Chapter 8.5, Problem 31E

To determine

To write: a recursive rule for the given sequence.

Answer to Problem 31E

  $a_n=a_{n-1}-10$ .

Explanation of Solution

Given:

The given sequence is $a_n=12-10n$ .

Calculation:

The given sequence is $a_n=12-10n$ .

Now, substitutes the value of $n=1,2,3,\mathrm{.....}\text{ and so on}$ . Therefore,

  $\begin{array}{l}{a}_n=12-10n\{\text{given sequences}}\\ a_1=12-10\left(1\right)\{\text{substitues }n=1\text{}}\\ a_1=2\\ a_2=12-10\left(2\right)\{\text{substitues }n=2\text{}}\\ a_2=-8\end{array}$

  $\begin{array}{l}\because a_n=a_{n-1}+d\\ \therefore a_2=a_{2-1}-10\\ \Rightarrow -8=2-10\left\{true\right\}\\ \therefore a_n=a_{n-1}-10\end{array}$

Hence, the recursive rule for the given sequence is $a_n=a_{n-1}-10$ .