<h3>
Answer: 540</h3>
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Explanation:
We have the arithmetic sequence {15, 18, 21, ...} and we want to add up the first n = 15 terms.
The first term is a = 15 and the common difference is d = 3
Plug these values into the arithmetic sum formula below
S = 0.5*n*(2*a + d(n-1))
S = 0.5*15*(2*15 + 3*(15-1))
S = 7.5*(30 + 42)
S = 7.5*(72)
S = 540
There are 540 seats total in the theater.
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The slower less efficient way to do this problem would be to list out the first 15 terms by hand like so
{15,18,21,24,27,30,33,36,39,42,45,48,51,54,57}
Then adding those fifteen terms up gives us
15+18+21+24+27+30+33+36+39+42+45+48+51+54+57 = 540
This helps confirm we have the correct answer.
