Cory Patrick

2022-06-24

What is the characteristic equation of ${a}_{n+2}+2{a}_{n}=0$?
So if we let ${a}_{n}=C{r}^{n}$ then we have $C{r}^{n+2}+2C{r}^{n}=C{r}^{n}\left({r}^{2}+2\right)$. So I got that the characteristic equation ${r}^{2}+2=0$ but it should be ${r}^{2}+2r=0$ apparently.

America Barrera

Expert

Step 1
The characteristic equation of :
${a}_{n+2}+\alpha {a}_{n+1}+\beta {a}_{n}=0$ is:
${r}^{2}+\alpha r+\beta =0$
Step 2
In your case $\alpha =0$ and $\beta =2$.

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