Chapter 1.1, Problem 39PPSE

Solution

To copy and complete the table given in the problem.

The table is completed incorporating the output of $5$ and the rule followed by the output:

Input	Output
$1$	$3$
$2$	$-1$
$3$	$-5$
$4$	$-9$
$5$	$-13$
$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$	$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$
$n$	$7-4n$

Given the table:

Input	Output
$1$	$3$
$2$	$-1$
$3$	$-5$
$4$	$-9$
$5$
$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$	$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$
$n$

Calculation:

Observe that the output of $1$ is $3$ : $3=7-4\cdot 1$ .

Again, the output of $2$ is $-1$ : $-1=7-4\cdot 2$ .

Analysing the table in a similar way, it may be observed that the output of $n$ follows the rule $7-4n$ .

Then, the output of $5$ :

  $7-4\cdot 5=-13$ .

Now, complete the table incorporating the output of $5$ and the rule followed by the output:

Input	Output
$1$	$3$
$2$	$-1$
$3$	$-5$
$4$	$-9$
$5$	$-13$
$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$	$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$
$n$	$7-4n$

Conclusion:

The table is completed incorporating the output of $5$ and the rule followed by the output:

Input	Output
$1$	$3$
$2$	$-1$
$3$	$-5$
$4$	$-9$
$5$	$-13$
$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$	$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$
$n$	$7-4n$