For an increasing sequence of numbers, how many other sequences could this be the average sequence of.
Where the average sequence, a = 0.5( s + s[i+1] )
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?
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?