Let a1=3 and a(n+1) =($\displaystyle {a}^{2}n+10$)/7 for every n$\displaystyle \geq$1

Prove by induction that 2$\displaystyle \leq$an$\displaystyle \leq$5 for every n$\displaystyle \geq$1

Deduce that an+1$\displaystyle \leq$an for every n$\displaystyle \geq$1

Show the sequence {an} converges and determine its limit.