Chapter 8.2, Problem 39HP

To determine

To explain: arithmetic sequences could be used to make real world predictions.

Explanation of Solution

For example, a person started to save 10 rupees on first day, and increasing that amount by 5 rupees per day. So how many days will it take to reach 30 rupees?

This problem can be solved by using arithmetic sequences.

First, need to describe the sequence

In this case, 10, 15, 20, …

The difference of the term numbers is 1.

  

Term number $\left(n\right)$	1	2	3
Term $\left(t\right)$	10	15	20

  

The common difference of the terms is 5.

This suggests that $t=5n$ , however need to add 5 to get the value of $t$ .

Therefore, the equation that describes the sequence is $t=5n+5$

To find $n$ , if $t=30$

  $\begin{array}{c}30=5n+5\\ 30-5=5n\\ \frac{25}{5}=n\\ n=5\end{array}$

Therefore, in 5 days he will save 30 rupees.

Like this, arithmetic sequences are used to make real world predictions.