Chapter 1.5, Problem 17HP

To determine

Find Tyler will have exactly 504 cards in his collection.

Answer to Problem 17HP

No

Explanation of Solution

Given:

Tyler has 23 base ball cards in his collection. Each week he buys a package with 8 cards to add to his collection. If Tyler continues in this way, will he ever have exactly 504 cards in his collection? Explain you reasoning.

Concept Used:

This is an arithmetic sequence.

The first term $a_1=23$ and the common difference is $d=8$ ; n is the number of weeks.

The nth term formula for arithmetic sequence is $a_n=a_1+d(n-1)$

Calculation:

  $\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_1=23;d=8\text{and}{a}_n=504,\text{find}n\\ 504=23+(n-1)·8\\ 504=23+8n-8\\ 504=15+8n\\ 504-15=15-15+8n\\ 489=8n\\ \frac{489}{8}=\frac{8n}{8}\Rightarrow n=61.125\end{array}$

Thus, No he will not able to collect exactly 504 cards, because the number of weeks cannot be a decimal number.