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Question Number 154668 by EDWIN88 last updated on 20/Sep/21

$$Iff\left(x\right)=f(x-1)+f(x+1)where$$$$f\left(10\right)=6andf\left(20\right)=2f\left(21\right)$$$$thenf\left(16\right)=\dots ?$$

Commented by mathdanisur last updated on 20/Sep/21

$$\mathrm{f}\left(16\right)=-\mathrm{f}\left(21\right)$$$$\mathrm{f}\left(21\right)=-6\Rightarrow \mathrm{f}\left(16\right)=6$$

Commented by Rasheed.Sindhi last updated on 20/Sep/21

$$Moredetailsplease!$$

Answered by Rasheed.Sindhi last updated on 20/Sep/21

$$f\left(x\right)=f(x-1)+f(x+1)$$$$f\left(x\right)-f(x-1)=f(x+1)$$$$Applyingdefinitiononleftside:$$$$f\left(x\right)-f(x-1)=f\left(x\right)+f(x+2)$$$$f(x-1)=-f(x+2)$$$$x-1\to x$$$$f\left(x\right)=-f(x+3)$$$$▸f\left(10\right)=-f\left(13\right)=6\Rightarrow f\left(13\right)=-6$$$$▸f\left(13\right)=-f(13+3)=-6$$$$f\left(16\right)=6$$

Commented by mathdanisur last updated on 20/Sep/21

$$\mathrm{Very}\mathrm{nice}\mathrm{Ser}$$

Commented by Rasheed.Sindhi last updated on 20/Sep/21

$$\mathcal{T}hanksser!$$

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