Chapter 8.2, Problem 41HP

To determine

To write:A rule using n and t to describe the sequence 7,8,9,10,....

Answer to Problem 41HP

The equation that describes the sequence is $t=n+6$

Explanation of Solution

Giveninformation:

Consider the equation y=x+6 represents the function {(1,7),(2,8),(3,9),(4,10)}

Need to write a rule using n and t to describe the sequence 7,8,9,10,....

Make a table to describe above sequence

The difference of the term numbers is 1

  

The common difference of the terms is 1

The terms have a common difference 1

This suggests that t=n, however need to add 6 to get the value of t.

Therefore, the equation that describes the sequence is $t=n+6$

Consider $y=x+6$

If $x=1$

Then $y=1+6$

  $y=7$

If $x=2$

Then $y=2+6$

  $y=8$

If $x=3$

Then $y=3+6$

  $y=9$

If $x=4$

Then $y=4+6$

  $y=10$

For input values 1,2,3 and 4 output values are 7,8,9 and 10.

Consider $t=n+6$

If $n=1$ ,

Then $t=1+6$

  $t=7$

If $n=2$

Then $t=2+6$

  $t=8$

If $n=3$

Then $t=3+6$

  $t=9$

If $n=4$

Then $t=4+6$

  $t=10$

For input values 1,2,3 and 4 output values are 7,8,9, and 10

Therefore, for both functions input values 1,2,3 and 4 output values are 7,8,9, and 10.