<ol class="abc-list"><li><div class="list-item-paragraph">An <strong>arithmetic</strong> sequence is such that each term in the sequence is found by adding the same number to the previous term. The first five terms of an arithmetic sequence are given by</div><div class="list-item-paragraph" style="text-align: center">$a$, $1$, $b$, $c$, $13$, ….</div><ol class="i-list"><li><div class="list-item-paragraph">Find the values of $a$, $b$ and $c$.</div></li><li><div class="list-item-paragraph">Find an expression, in terms of $n$, for the ${{n}^{\mathrm{th}}}$ term, ${{T}_{n}}$, of this arithmetic sequence.</div></li><li><div class="list-item-paragraph">Explain why the terms of the sequence are all odd numbers.</div></li></ol></li><li><div class="list-item-paragraph">Observe the following difference of unit fractions.</div><div class="list-item-paragraph" style="text-align: center">${\textbf{1}^{\mathrm{st}}\ \mathrm{line:}\ 1 - \frac{1}{2} = \frac{1}{2}}$</div><div class="list-item-paragraph" style="text-align: center">${\textbf{2}^{\mathrm{nd}}\ \mathrm{line:}\ \frac{1}{2} - \frac{1}{3} = \frac{1}{6}}$</div><div class="list-item-paragraph" style="text-align: center">${\textbf{3}^{\mathrm{rd}}\ \mathrm{line:}\ \frac{1}{3} - \frac{1}{4} = \frac{1}{12}}$</div><div class="list-item-paragraph" style="text-align: center">${\vdots}$</div><div class="list-item-paragraph" style="text-align: center">${\textbf{10}^{\mathrm{th}}\ \mathrm{line:}\ \frac{1}{10} - \frac{1}{11} = \frac{1}{110}}$</div><div class="list-item-paragraph" style="text-align: center">${\vdots}$</div><ol class="i-list"><li><div class="list-item-paragraph">Write down the ${{4}^{\mathrm{th}}}$ line and the ${{5}^{\mathrm{th}}}$.</div></li><li><div class="list-item-paragraph">Write down an expression of the ${{n}^{\mathrm{th}}}$ line.</div></li><li><div class="list-item-paragraph">Does the term $\frac{1}{421}$ exists in row $n$? Justify your answers with working.</div></li><li><div class="list-item-paragraph">By adding the first $3$ lines, we obtain $1-\frac{1}{4}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}$. Thus, $1=\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{12}$.</div><div class="list-item-paragraph">Using this information, express 1 as a sum of seven different unit fractions.</div></li></ol></li></ol>

An **arithmetic** sequence is such that each term in the sequence is found by adding the same number to the previous term. The first five terms of an arithmetic sequence are given by

Observe the following difference of unit fractions.

${\textbf{1}^{\mathrm{st}}\ \mathrm{line:}\ 1 - \frac{1}{2} = \frac{1}{2}}$

${\textbf{2}^{\mathrm{nd}}\ \mathrm{line:}\ \frac{1}{2} - \frac{1}{3} = \frac{1}{6}}$

${\textbf{3}^{\mathrm{rd}}\ \mathrm{line:}\ \frac{1}{3} - \frac{1}{4} = \frac{1}{12}}$

${\textbf{10}^{\mathrm{th}}\ \mathrm{line:}\ \frac{1}{10} - \frac{1}{11} = \frac{1}{110}}$

IP1U7 Exercise Q9

IP1U7 Exercise Q9

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