Each time a touchdown is scored at 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. \( A(n) = 12 + 6n \)
B. \( A(n) = 12 - (n - 1)6 \)
C. \( A(n) = 12 + (n - 1) \)
D. \( A(n) = 12 + (n - 6) \)
Answer (3)
If the team already had 12 points and it gains points for a touch down you know that both have to be positive. if a team scores 2 touchdowns then this is multiplied by 6 and added to 12 so it has to be 6 multiplied by the number of touchdowns. so A(n) = 12 + 6n
The correct rule representing the number of points as an arithmetic sequence is A(n)=12+6n, where n is the number of touchdowns scored beyond the initial 12 points the team already has, with each touchdown contributing an additional 6 points to the score.
The question asks which rule represents the number of points as an arithmetic sequence when n is the number of touchdowns scored, assuming each touchdown is worth 6 points and the team already has 12 points. The correct formula for an arithmetic sequence is A(n)=12+6n, where n represents the number of additional touchdowns scored beyond the current score.An arithmetic sequence has the form A(n) = A(1) + (n-1)d, where A(1) is the first term and d is the common difference between terms. In this scenario, A(1) equals the initial 12 points and d equals 6 points (the points awarded for each touchdown). Thus, after n touchdowns, the total score would be the initial score plus 6 times the number of touchdowns.Therefore, the correct answer is A(n)=12+6n. This formula can be used to calculate the total score of the team after any number of additional touchdowns scored.
The formula representing the number of points as an arithmetic sequence when scoring touchdowns is A ( n ) = 12 + 6 n . This indicates that for every touchdown scored, the team earns an additional 6 points. Therefore, the correct answer is option A.
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