Question

traingular numbers can be modeled by a function suggested in the diagram. if you duplicate each triangular number on top of itself, you can partition the resulting arrangement into an n by square and a 1 by n now. Graph the function f(n)=1/2(n^2+n) and y=91 to determine which triangular number 91 is. Use your graph to communicate why any intersection points may be a solution to the equation, but now a reasonable solution to the problem.

Answer 1

(13,91)

Explanation:

f(n) = ½(n² + n) = 91

n² + n = 182

n² + n - 182 = 0

n² + 14n - 13n - 182 = 0

n(n + 14) - 13(n + 14) = 0

(n - 13)(n + 14) = 0

n = 13, -14(not possible)

n = 13

Answer 2

n =13

Explanation:

Solve for [ n(n+1) ]/2 = 91

=> n^2 +n -182 = 0

=> (n-13)(n+14)=0

=> n=13 ( n = -14 is not valid)