QUESTION $3$

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$3\mathrm{.}1$ Given: The sum of the first $n$ terms of the series is given as $S_n=n^2+2n-1.$ Determine the first three terms of the series.

$3\mathrm{.}2$ Given:

${\displaystyle \underset{n=0}{\overset{k}{}}}2(3{)}^{n-1}=2186\frac{2}{3}$

$3\mathrm{.}2\mathrm{.}1$ Determine the first three terms of the series.

$3\mathrm{.}2\mathrm{.}2$ Determine if the series has a constant difference or a constant ratio, as well as the value of it$.$

$3\mathrm{.}2\mathrm{.}3$ Calculate the value of $k.$