An architect designs a theater with 15 seats in the first row, 18 in the second, 21 in the third, and so on. If the theater is to have a seating capacity of 870, how many rows must the architect use in his design?

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Answer 1 · 2018-07-19T04:10:32

20 rows

Write a formula to illustrate this arithmetic sequence:
$a_n= 15+3(n-1)$

Using the sum formula:
$870= n/2(15+15+3(n-1))$

$1740=3n^2+27n$

$1740= 3(n^2+9n)$

$580= n^2+9n$

$n^2+9n-580=0$

$(n+29)(n-20)=0$

$n=20$