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!