Let a0 and a1 be distinct real numbers

Set an=(an-1+an-2)/2 for each n>=2

Use induction to show that:

an+1-an=(-1/2)^n*(a1-ao)

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If we take fore n=2...a2=a1+a0/2

And then a3=(((a1+a0)/2)+(a1))/2

So a3-a2 should be equal to that WALBOA

The problem I'm having is how to show that P(n)--> P(n+1)

You can assume this is true for n, but I don't know how to show it true for n+1