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**delgeezee** I keep confusing myself when I try and do this.

Let $\displaystyle a_{1}$ and $\displaystyle a_{0}$ be distinct real numbers. Define $\displaystyle a_{n} = \frac{a_{n-1} + a_{n-2}}{2}$ for positive integers $\displaystyle n \geq 2$ . Show $\displaystyle a_{n+1} - a_{n } = (-\frac{1}{2})^{n}(a_{1}- a_{0}) $

I show when n =1 is true $\displaystyle a_{2} - a_{1 } = (-\frac{1}{2})^{1}(a_{1}- a_{0}) $

=> $\displaystyle a_{2} - a_{1 } = (-\frac{1}{2})}(a_{1}- a_{0}) $

Then I must assume n = k is true, and show for n = k+1 is true.

However I keep wanting to reduce into terms of $\displaystyle a_{1}$ and $\displaystyle a_{0}$ and I get mixed up and forget what Im trying to do.