- #1

trollcast

Gold Member

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## Homework Statement

For an increasing sequence of numbers, how many other sequences could this be the average sequence of.

## Homework Equations

Where the average sequence, a

*= 0.5( s*

*+ s[i+1] )*

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## 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?The lowest difference here is 2 so theres 2 possible sequences for which s is the average of?