SOLUTION: Determine how many rows are in the corner section of a stadium containing 3920 seats if the
first row has 10 seats and each successive row has 6 additional seats?
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first row has 10 seats and each successive row has 6 additional seats?
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Question 1186348: Determine how many rows are in the corner section of a stadium containing 3920 seats if the
first row has 10 seats and each successive row has 6 additional seats? Answer by ikleyn(52803) (Show Source):
It is about finding the number of terms of an arithmetic progression, when its
first term, the common difference and the sum of n terms are given.
The formula for the sum of n first terms of an AP is
= ,
In this problem, = 10, d = 6. So your equation is
= 3920.
Multiply both sides by 2
(20 + 6*(n-1))*n = 7840
20n + 6n^2 - 6n = 7840
6n^2 + 14n - 7840 = 0.
Apply the quadratic formula and find the roots.
You will get two roots. One root is negative, and we reject it.
The other root is positive, and its value is 35.
It is the solution to the problem.
ANSWER. 35 rows.
