Question

A basketball team has a halftime promotion where a fan gets to shoot a 3-pointer to try to win a jackpot. The jackpot starts at \(5000 for the first game and increases \)500 each time there is no winner. Ken has tickets to the fifteenth game of the season. How much will the jackpot be for that game if no one wins by then?

Short answer

The jackpot for the fifteenth game if no one wins by then is$12000.

Step-by-step solution

Step 1. Given Information.

Given a basketball team has a halftime promotion where a fan gets to shoot a 3-pointer to try to win a jackpot. The jackpot starts at $5000 for the first game and increases $500 each time there is no winner. Ken has tickets to the fifteenth game of the season.

Step 2. Calculation.

The jackpot here forms an arithmetic sequence as it constantly increases at a rate of $500.

The n^th term of an arithmetic sequence is given by $a_n=a_1+\left(n-1\right)d$.

Here the first term is $a_1=5000$

The common difference is $d=500$

And the required term is n=15

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ a_{15}=5000+\left(15-1\right)\left(500\right)\\ a_{15}=5000+\left(14\right)\left(500\right)\\ a_{15}=5000+7000\\ a_{15}=12000\end{array}$

Step 3. Conclusion.

Hence, the jackpot for the fifteenth game if no one wins by then is $12000.