Chapter 7.8, Problem 59MR

To determine

To write the recursive and explicit formulas for the arithmetic sequence $0,9,18,27,\mathrm{........}$

Answer to Problem 59MR

Recursive formula is $a_1=0;a_n=a_{n-1}+9$ & explicit formula is $a_n=9n-9$ .

Explanation of Solution

Given information:

  $0,9,18,27,\mathrm{........}$

Calculation:

The first tem of the given arithmetic sequence is $a_1=0$ and the common difference is $d=9-0=9$ .

Now recursive formula is,

  $\begin{array}{l}{a}_1=a;a_n=a_{n-1}+d\\ \Rightarrow a_1=0;a_n=a_{n-1}+9\end{array}$

And the explicit formula is,

  $\begin{array}{l}{a}_n=a+\left(n-1\right)d\\ \Rightarrow a_n=0+\left(n-1\right)\cdot 9\\ \Rightarrow a_n=9n-9\end{array}$