Expert: Sherman D. - 10/26/2007

Question
I'm having trouble with this problem:

Let a, b, c, d, and e be the unique rational numbers satisfying the system of equations:

2 = a + b + c + d + e
4 = 16a + 8b + 4c + 2d + e
6 = 81a + 27b + 9c + 3d + e
8 = 256a + 64b + 16c + 4d + e
34 = 625a + 125b + 25c + 5d + e

Determine a - b + c - d + e

Answer
2 = a + b + c + d + e
4 = 16a + 8b + 4c + 2d + e
6 = 81a + 27b + 9c + 3d + e
8 = 256a + 64b + 16c + 4d + e
34 = 625a + 125b + 25c + 5d + e

e = -a - b - c - d + 2
e = -16a - 8b - 4c - 2d + 4
e = -81a - 27b - 9c - 3d + 6
e = -256a - 64b - 16c - 4d + 8
e = -625a - 125b - 25c - 5d + 34

as far as i can tell there's a pattern

e = -(1^4)a - (1^3)b - (1^2)c - (1^1)d + (1*2)
e = -(2^4)a - (2^3)b - (2^2)c - (2^1)d + (2*2)
e = -(3^4)a - (3^3)b - (3^2)c - (3^1)d + (3*2)
e = -(4^4)a - (4^3)b - (4^2)c - (4^1)d + (4*2)
e = -(5^4)a - (5^3)b - (5^2)c - (5^1)d + (17*2)

that 34 is the only one that doesn't fit the pattern.

sorry thats about all i get out of it. Check with answers.yahoo.com for help.