Posted by Riana on Sunday, January 27, 2013 at 1:42am.
Solve using aritmetic progression and quadratic equation, how?
Sum of AP = n/2(2a+(n-1)d)
Where n is the number of terms, ie in your case the number of rows of seats, 'a' is the number in the first row (a=262) and 'd' is the difference in the next row (d=18). Sum of AP is the number of seats in the arena (Sum=15690). Put this together and you get:
15690=n/2[2*262+(n-1)18]
18n^2+506n-31380=0
equation to: ax^2+bx+c,; a=18, b=506, c=-31380
Now comes the quadratic, solution to a quadratic =
[-b(+/-)Sqrt(b^2-4ac)]/2a
substitute the values of a,b anc from above into the quadratic and solve.
n=30.
Please always check your answer, in this case use sum of AP.
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