Chapter 1, Problem 1RE

In Exercises 1-8, use inductive reasoning to predict the next three numbers or figures in the pattern.

1, 3, 8, 13, 18_{, ....}

To determine

To predict: The next three numbers following the pattern.

Answer to Problem 1RE

The next three numbers for the pattern are $23,28,33$.

Explanation of Solution

Given:

The pattern is $3,8,13,18,\cdots$.

Calculation:

From the given pattern, it is observed that numbers in the pattern are found by adding 5 to the previous.

$\begin{array}{l}3+5=8\\ 8+5=13\\ 13+5=18\end{array}$

The last number is given as 18.

Thus, to continue the pattern, add 5 to number 18 and obtain that $18+5=23$.

Use the same method and find the next two numbers.

Thus, add 5 to the obtained result 23 and discover the next number in the pattern as $23+5=28$.

Similarly, add 5 to the obtained result 23 and discover the next number in the pattern as $28+5=33$.

Hence, the next three numbers for the pattern are $23,28,33$.