Question

If Φ (r)= 2^r, show that Φ (r+1) =2 Φ(r).

Answer 1

$Φ (r)= 2^r,$

then $\Phi(r+1)=2^{r+1}=2^r\cdot2^1=2\cdot2^r=2\Phi(r),$

so the statement $Φ (r+1) =2 Φ(r)$ holds.