# Solving an recursive sequence [closed]

I have an recursive sequence and want to convert it to an explicit formula.

The recursive sequence is:

$$f(0) = 4$$

$$f(1) = 14$$

$$f(2) = 194$$

$$f(x+1) = f(x)^2 - 2$$

## closed as off-topic by Steven Landsburg, user44191, RP_, David White, Piotr HajlaszMar 11 at 15:05

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## 1 Answer

$$f(x+1) = f(x)^2 - 2,\;\;f(0)=4$$ $$\Rightarrow f(x)=2\cos\left(2^x\arccos 2\right)=2 \cosh \left(2^x \ln \left(\sqrt{3}+2\right)\right)$$

• sorry i forgot to say that --> f(0) = 4 – raimannma Mar 11 at 13:28
• perfect thank you very much – raimannma Mar 11 at 13:57