Chapter 8, Problem 14CT

To determine

Give the explanation for the given statement.

Answer to Problem 14CT

The given statement represents the arithmetic sequence.

Explanation of Solution

Given:

The given statement is that a company donate $\$5000$ to a charity plus $\$100$ for each home run hit by the local team.

Calculation:

In an arithmetic sequence, the difference of consecutive terms, called the common difference, is constant.

The $n\text{th}$ term of the arithmetic sequence is $a_n=a_1+\left(n-1\right)d$ , where $a_1$ is the first term and $d$ is the common difference.

In the given statement $a_1=5000$ and $d=100$ .

  $a_n=5000+\left(n-1\right)100$

The recursive form is $a_n=a_{n-1}+d$

  $a_n=a_{n-1}+100$

Hence the given statement represents the arithmetic sequence.