SOLUTION: What is the equation of the problem when the number sequence is: 1, 3, 6, 10?

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Question 302042: What is the equation of the problem when the number sequence is: 1, 3, 6, 10?
Found 2 solutions by scott8148, richwmiller:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
the 2nd level differences are constant (differences of differences), so this is a second order (squared) relation

a = xn^2 + yn + z

A) substituting for n=1 ___ 1 = x + y + z

B) substituting for n=2 ___ 3 = 4x + 2y + z

C) substituting for n=3 ___ 6 = 9x + 3y + z

subtracting A) from B) ___ 2 = 3x + y ___ 2 - 3x = y

subtracting A) from C) ___ 5 = 8x + 2y

substituting ___ 5 = 8x + 2(2 - 3x) ___ 5 = 8x + 4 - 6x ___ 1 = 2x ___ 1/2 = x

substituting ___ 2 - 3(1/2) = y ___ 1/2 = y

substituting ___ 1 = (1/2) + (1/2) + z ___ 0 = z

the equation is ___ a = (1/2)(n^2 + n)

Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
0+1=1
1+2=3
3+3=6
6+4=10
a+n=a sub (n+1)
where a is the last number and n is the place