Question

(I typed it wrong the 1st time)

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 in the theater?​​

Answer 1

Answer: 540

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Step-by-step 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.