How am I meant to solve B? I've done A it goes as follows:-
Sequences may be generated by recurrence relations of the form $U_{n+1}=kU_n-20, U_0=5.$
A) Show that $U_2=5k^2-20k-20$
B) Determine the range of values of K for which $U_2 \lt U_0.$
Thanks.
You want to find the values of $k$ for which $U_2 < U_0$:
$U_2 < U_0 \Leftrightarrow 5k^2-20k-20 < 5 \Leftrightarrow k^2 -4k-4 < 0$
Do you get how to solve the rest?