Chapter 7, Problem 18TP

Solution

To state: If it makes more sense to represent this situation using a sequence or a series. If during a baseball season, a company pledges a donation to a charity of $5000 plus $100 for every home run hit by the local team.

The situation makes more sense to represent this situation using a sequence.

Given information:

A company pledges a donation to a charity of $5000 plus $100 for every home run hit by the local team.

Explanation:

A company pledges a donation to a charity of $5000. Then the first term is $a_1=5000$ .

For every home run hit by the local team there is additional $100. Then the second term will be:

  $\begin{array}{c}{a}_1+500=5000+500\\ =5500\end{array}$

Similarly, the third term will be:

  $\begin{array}{c}{a}_3=a_2+500\\ =a_1+2\cdot 500\\ =6000\end{array}$

Now observe that the nth term depends on the first term, and the number of home run hit.

Thus the general rule will become:

  $a_n=a_1+500\cdot \left(n-1\right)$

It can be seen that it is a general term for an arithmetic sequence. It means that it makes more sense to represent this situation using a sequence