1. Each time a touchdown is scored in a football game, 6 points are added to the score of the scoring team. A team already has 12 points. What rule represents the number of points as an arithmetic sequence when n is the number of touchdowns scored?

A(n) = 12 + 6n
A(n)12 - (n - 1)(6)
A(n) = 12 + (n - 1)(6)
A(n) = 12 + (n - 6)

2. What is the ninth term of the arithmetic sequence defined by the rule A(n) = -14 + (n - 1)(2)?

232
230
2
4

Please explain how to do these! I don't understand them!

are the answers:

1. A(n) = 12 + (n - 1)(6)
2. 2

1. assuming the 12 points were scored by 2 touchdowns, (could have been 4 fieldgoals)

and n is the total number of touchdowns scored, it would be
A(n) = 12 + 6(n-2) , .... two have already been counted

if n is the number of touchdowns after the initial 12 points, it would be
A(n) = 12 + 6n

poorly worded question.

2.
A(n) = -14 + (n-1)(2)
so a = -14 and d = 2

term(9) = a+8d
= -14 + 8(2) = 2

42

Use the following information.

SPORTS In a football game, each team earns 6 points for each touchdown it scores.




Write an equation to find y, the total number of points for scoring x touchdowns.

Use symbols to describe the value of each term as a function of its position. Then find the twelfth term in each sequence.

Sure! I'd be happy to explain these questions to you.

1. Each time a touchdown is scored in a football game, 6 points are added to the score of the scoring team. In this case, we are given that the team already has 12 points. We want to find a rule that represents the number of points as an arithmetic sequence when n is the number of touchdowns scored.

To solve this, we need to find a relationship between the number of touchdowns scored (n) and the total number of points (A(n)).

Since each touchdown scores 6 points, we can start with the initial number of points (12) and add 6 points for each touchdown scored. This gives us the rule:

A(n) = 12 + 6n

So, option 1 (A(n) = 12 + 6n) represents the correct rule.

2. The second question asks for the ninth term of the arithmetic sequence defined by the rule A(n) = -14 + (n - 1)(2).

In an arithmetic sequence, each term is obtained by adding a constant difference (d) to the previous term. In this case, the rule A(n) = -14 + (n - 1)(2) gives us the formula to find the nth term.

To find the ninth term, we can substitute n = 9 into the formula:

A(9) = -14 + (9 - 1)(2)
A(9) = -14 + (8)(2)
A(9) = -14 + 16
A(9) = 2

Therefore, the ninth term of the sequence is 2.

So, the correct answer is option 2 (2).

I hope this helps you understand these concepts better. Let me know if you have any more questions!