5=160
100 143 162 165 160
43 19 3 -5 (first difference)
24 16 8 (2nd difference)
Muhammed Rashad
Grade 7
Winchester Public School
Toronto
Canada
+129840
Let's see how Muhammed may have arrived at his answer
100 143 162 165 160
43 19 3 -5 (first difference)
24 16 8 (second difference)
8 8
We have three non-zero differences, so we will have a 3rd power polynomial =
Ax^3 + Bx^2 + Cx + D
And we will have this system of equations
729A + 81 B + 9 C + D = 100
512A + 64B + 8C + D = 143
343A + 49B + 7 C + D = 162
216A + 36B + 6C + D = 165
Using a matrix solver we have that :
A = -4/3 , B = 20, C = -28/13, D = 295
So ....our polynomial is
(-4/3)x^2 + 20x^2 - (28/13)x + 295
And when x = 5, this evaluates to 160
