1. The problem statement, all variables and given/known data For an increasing sequence of numbers, how many other sequences could this be the average sequence of. 2. Relevant equations Where the average sequence, a = 0.5( s + s[i+1] ) 3. The attempt at a solution If theres n terms in the original sequence. The number of differences between consecutive terms is (n - 1) Find all these, (n-1) and find the lowest difference. Then this lowest difference + 1 is your answer? eg. s = 1, 3, 6, 10, 12 s[i+1] - s = 2, 3, 4, 2 The lowest difference here is 2 so theres 2 possible sequences for which s is the average of?