2022 RI P1 Q6
(a)
A sequence is such that ${{u}_{1}}=p$, where $p$ is a constant, and ${{u}_{n+1}}=\frac{4}{{{u}_{n}}}$, for $n>0$.
Describe how the sequence behaves when
(i) $p=2$,
[1]
(ii) $p=3$.
[1]
(b)
Another sequence ${{v}_{1}}$, ${{v}_{2}}$,${{v}_{3}}$ , … is such that ${{v}_{n}}={{v}_{n-1}}+n$, where $n\ge 2$, and ${{v}_{1}}=A$.
Find, in terms of $A$ and $n$, an expression for
(i) ${{v}_{n}}$,
[4]
(ii) $\sum\limits_{r=1}^{n}{{{v}_{r}}}$.
[3]
(You need not simplify your answer. You may use the result $\sum\limits_{r=1}^{n}{{{r}^{2}}=\frac{1}{6}n\left( n+1 \right)\left( 2n+1 \right)}$.)
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