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A theater has 20 seats in the first row and each row after has 4 more seats than the row before it. How many seats are in the theater if there are 15 rows of seats?

User Sazz
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1 Answer

4 votes

Answer:

660

Explanation:

its going to be an arithmetic series so write out the first few terms of thr first row then second row etc

20, 24, 28, 32...

the formula for an arithemtic series is Un = a + d(n-1) where a is the first term and d is the common difference

in this sequence, a = 20 and d = 4

so the nth term formula for this sequence is

Un = 20 + 4(n-1) where n is the number of the row

The sum formula of an arithmetic series is

Sn = 0.5n (2a+d(n-1))

in other words, Sn is the sum of n terms. e.g. if you wanted to find the sum of the first 5 rows tou could sum in n=5 as well as the a and d values from above instead of doing n1+n2+n3+n4 etc

sub in a=20, d=4 and n=15

total seats of 15 rows = (0.5x15)(2x20 + 4+14)

= 7.5 (40+48)

= 660

User Mikepurvis
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