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The first row of an auditorium has 42 seats. Each row after the first has three more seats than the row before it.

A.) write an equation for finding the number of seats in the nth row

I just need to know what the equation is pls

User Keepthepeach
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1 Answer

18 votes
18 votes

Answer:

42 + 3(n - 1)

Explanation:

We can model this situation with an arithmetic sequence where n is the row number.

Start off with the first row. We know that there are 42 seats to begin with. Since the starting value for this sequence won't change (unless someone breaks or adds another chair), we can represent it as a constant, or a coefficient without a variable.

# of seats in the 1ˢᵗ row = 42

Then, for each row after that, there are 3 more seats added. Since the total amount of seats added since the first row varies by each row, we have to use a variable to represent this change. The variable's coefficient represents the amount of seats added per row.

# of seats in the nᵗʰ row = 42 + 3n

However, this initial attempt is incorrect, as if we test it with the first row (when n = 1), we get 42 + 3(1), which is not equal to 42. We can account for this shifting in the + 3 (because we don't want to apply it to the first row) by subtracting 1 from n:

# of seats in the nᵗʰ row = 42 + 3(n - 1)

Finally, we can check this new equation to make sure it works:

42 ≟ 42 + 3(1 - 1)

42 ≟ 42 + 3(0)

42 = 42

User Domshyra
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