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Ksju [112]
2 years ago
5

In a theater, there are 15 chairs in the first row, each row has 3 more chairs than the previous row, and there are 15 rows. how

many chairs are there in the theater?
SAT
1 answer:
Nimfa-mama [501]2 years ago
5 0

The 1st row has 15 chairs.

The 2nd row has 15 + 3 = 18 chairs.

The 3rd row has 18 + 3 = 15 + 2•3 = 21 chairs.

The 4th row has 21 + 3 = 15 + 3•3 = 24 chairs.

The pattern continues, so that the n-th row has 15 + (n - 1)•3 = 3n + 12 chairs.

If there are 15 rows, then the total number of chairs is

\displaystyle \sum_{n=1}^{15} (3n + 12) = 3 \sum_{n=1}^{15} n + 12 \sum_{n=1}^{15} 1 = 3\cdot\frac{15\cdot16}2 + 12\cdot15 = \boxed{540}

where we use the formulas

\displaystyle \sum_{n=1}^N 1 = N

\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2

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