Chapter 4.5, Problem 28STP

To determine

The expression for $s\left(n\right)$ with respect to $n$ .

Answer to Problem 28STP

The required expression is $s\left(n\right)=\frac{1}{4}n+3$ .

Explanation of Solution

Given information:

The given table is

  

From the given table it is observed that at $n=0$ the value of $s\left(n\right)=3$ .

Thus, the expression must be in the form of,

  $s\left(n\right)=an+3$  ...... (1)

Here $a$ is a constant.

Now, to find the value of $a$ .

Substitute the value $a=-8$ and $s\left(n\right)=1$ in the equation (1).

  $1=a\left(-8\right)+3$

Now, solve for $a$ .

  $\begin{array}{c}1=a\left(-8\right)+3\\ -8a=-2\\ a=\frac{1}{4}\end{array}$

To find the value of $s\left(n\right)$ , substitute the value of $a$ in the equation (1).

  $s\left(n\right)=\frac{1}{4}n+3$

Hence, the required expression is $s\left(n\right)=\frac{1}{4}n+3$ .