Answer
Geometric;
$9831$
Work Step by Step
Let's note by $\{a_n\}$ the given sequence. The sum of its first $7$ terms is:
$$S_7=\sum_{n=0}^6 3(-4)^n=\sum_{k=1}^7a_k.$$
The terms of the sequence are:
$$\begin{align*}
a_1&=3(-4)^0\\
a_2&=3(-4)^1\\
a_3&=3(-4)^2\\
&\dots\\
a_7&=3(-4)^6.
\end{align*}$$
We notice that the common ratio of consecutive terms is $-4$, therefore constant, so the sequence is geometric with the elements:
$$\begin{cases}
a_1=3(-4)^0=3\\
d=-4.
\end{cases}$$
Calculate the partial sum $S_7$ using the formula:
$$S_n=\dfrac{a_1(1-r^n)}{1-r}.$$
For $n=7$ we have:
$$S_{7}=\dfrac{3\left(1-(-4)^7\right)}{1-(-4)}=9831.$$
