2022 CJC Promo Q4
It is known that the ${{n}^{\text{th}}}$ term of a sequence is given by ${{u}_{n}}=p\left( {{4}^{-n}} \right)+qn+r$, where $p$, $q$ and $r$ are constants.
It is given that ${{u}_{1}}=6$, ${{u}_{2}}=0$ and ${{u}_{3}}=-\frac{15}{4}$.
(i)
Find $p$, $q$ and $r$.
[3]
(ii)
Show $\sum\limits_{r=1}^{n}{{{u}_{r}}}=A+B\left( {{4}^{-n}} \right)+Cn+D{{n}^{2}}$ where $A$, $B$, $C$ and $D$ are constants to be determined.
[4]
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