Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.

Question

Recall that the Fibonacci sequence is defined by $F_0=0, F_1=1$ and $F_n =F_n−1 +Fn−2$, for $n\geq 2$.

Prove that for all $n\geq 1$ we have $F_n<{\left(\frac 74\right)}^n$.