<p>The sum, ${{S}_{n}}$, of the first $n$ terms of a sequence ${{u}_{1}}$, ${{u}_{2}}$,${{u}_{3}}$, … is given by ${{S}_{n}}={{n}^{2}}\left( An+B \right)$, where $A$ and $B$ are non-zero constants.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find an expression for ${{u}_{n}}$ in terms of $A$, $B$ and $n$, simplifying your answer.</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">It is also given that the second term is $6$ and the sixth term is $218$. Find the values of $A$ and $B$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Determine if the sum to infinity exists.</div><p style="text-align: right;">[1]</p></li></ol>

The sum, ${{S}_{n}}$, of the first $n$ terms of a sequence ${{u}_{1}}$, ${{u}_{2}}$,${{u}_{3}}$, … is given by ${{S}_{n}}={{n}^{2}}\left( An+B \right)$, where $A$ and $B$ are non-zero constants.

Find an expression for ${{u}_{n}}$ in terms of $A$, $B$ and $n$, simplifying your answer.

It is also given that the second term is $6$ and the sixth term is $218$. Find the values of $A$ and $B$.

RI Sequences and Series tutorial 7A Q5

RI Sequences and Series tutorial 7A Q5

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