The sum of the first $n$ terms of a sequence is given by $S_{n} = 6 - \dfrac{3^{n+1}}{2^{n-1}}$.

Question

The sum of the first $n$ terms of a sequence is given by $S_{n} = 6 - \dfrac{3^{n+1}}{2^{n-1}}$. State the first term and prove that the series is a geometric series. Thus, state the common ratio.

Accepted Answer

First term $= -3$, $\displaystyle r = \frac{3}{2}$

Sequence and Series - Proving the progression

Sequence and Series - Proving the progression

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