Chapter 3.6, Problem 7WE

To determine

To find: the next two numbers in the given sequence

Answer to Problem 7WE

The next two numbers in the given sequence are $15,4$

Explanation of Solution

Given information: The sequence is $40,39,36,31,24,\mathrm{...}$

Calculation:

Let the next two numbers in the sequence be x and y

Consider the sequence $40,39,36,31,24,x,y$

First find the relationship between the terms

  $\begin{array}{l}40-39=1\\ 39-36=3\\ 36-31=5\\ 31-24=7\end{array}$

Here, it can be observed that the difference between the terms forms a pattern $1,3,5,7,\mathrm{...}$ such that the difference between the terms in this pattern is 2. So, the next two terms in the sequence $1,3,5,7,\mathrm{...}$ must be $7+2=9,\text{}\text{}9+2=11$

Now find x and y.

As per the pattern followed above,

$24-x$ should be equal to $9$

  $\begin{array}{l}24-x=9\\ \Rightarrow x=24-9=15\end{array}$

Also,

$x-y$ should be equal to $11$ that is $x-y=11$

Put $x=15$

  $\begin{array}{l}x-y=11\\ \Rightarrow 15-y=11\\ \Rightarrow y=15-11=4\end{array}$