SOLUTION: Hello! I've been trying to solve this problem- it goes as shown: For a particular sequence, each term is the sum of the three preceding terms. If a, b, c, d, e, 0, 1, 2, 3 are cons

Question 1153131: Hello! I've been trying to solve this problem- it goes as shown: For a particular sequence, each term is the sum of the three preceding terms. If a, b, c, d, e, 0, 1, 2, 3 are consecutive terms of this sequence, what is the value of a + b + c + d + e?
My attempts to solve this have gone as follows:
Since the 8th term (2) is the sum of e + 0 + 1, e must be 1, as that would be the only solution to this. I worked backwards from there: 1 = 0 + 1 + d, so d must be 0. This is where my reasoning failed. I thought c was equal to -1, which meant that b must be 2, and a must be -1. However, since the only term preceding b is -1, I thought b must be -1, too.
Is it wrong of me to think the sequence must start on a? Is it implied that the sequence goes much further backwards?
Thank you in advance for any and all help!
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!

Unless otherwise specified, you are correct to assume the sequence starts at 'a' (so while working backwards, a+b+c=d is the last valid equation you can write).

Your answer looks correct: -1,2,-1,0,1,0,1,2,3

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