Chapter 8.2, Problem 38HP

To determine

To find: the number of multiples of 6 between 41 and 523.

Answer to Problem 38HP

The number of multiples of 6 between 41 and 523 is 81.

Explanation of Solution

Calculation:

Multiples of 6 between 41 and 523 are

42, 48, 54, 60, …, 522

Make a table to describe the sequence.

The difference of the term numbers is 1.

  

Term number $\left(n\right)$	1	2	3	4
Term $\left(t\right)$	42	48	54	60

  

The common difference of the terms is 6.

Since, the common difference of the terms is 6

This suggests that $t=6n$ , however need to add 36 to get the value of $t$ .

Therefore, the equation that describes the sequence is $t=6n+36$

To find $n$ , if $t=522$

  $\begin{array}{c}522=6n+36\text{Replace}t\text{with}522\\ 522-36=6n\\ 486=6n\\ \frac{486}{6}=n\\ 81=n\end{array}$

Therefore, the number of multiples of 6 between 41 and 523 is 81.