Answer
Geometric;
$4.68559$
Work Step by Step
Let's note by $\{a_n\}$ the given sequence. The sum of its first $6$ terms is:
$$S_6=1+0.9+(0.9)^2+\dots+(0.9)^5.$$
The terms of the sequence are:
$$\begin{align*}
a_1&=1\\
a_2&=0.9\\
a_3&=(0.9)^2\\
&\dots\\
a_6&=(0.9)^5.
\end{align*}$$
We notice that the common ratio of consecutive terms is $0.9$, therefore constant, so the sequence is geometric with the elements:
$$\begin{cases}
a_1=1\\
r=0.9.
\end{cases}$$
Calculate the partial sum $S_6$ using the formula:
$$S_n=\dfrac{a_1(1-r^n)}{1-r}.$$
For $n=6$ we have:
$$S_6=\dfrac{1(1-(0.9)^6}{1-0.9}=4.68559.$$
