$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}
\end{cases}
\\\\\\
\sum\limits_{n=1}^{8}~-2(3)^{n-1}~~
\begin{cases}
n=8\\
a_1=-2\\
r=3
\end{cases}\implies S_8=-2\left( \cfrac{1-3^8}{1-3} \right)
\\\\\\
S_8=\underline{-2}\left( \cfrac{1-6561}{\underline{-2}} \right)\implies s_8=1-6561\implies S_8=-6560$

8 0

3 years ago

Paisley's car used 11 gallons to travel 374 miles. How many gallons of gas would she need to travel 442 miles?

katen-ka-za [31]

Answer:

13 gallons

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Given I have multiplication of integers, with an odd amount of neg(-) signs what; is the sign of my final answer?

storchak [24]

The answer of the final sign should be negative

7 0

3 years ago

bird that was perched atop a 15 ½ foot tree dives down six feet to a branch below. How far above the ground is the bird’s new lo

never [62]

Answer:

ok so if the bird is on the top at 15 and a half then goes down six feet substrate 15 and a half from six and you get nine and half from the ground to the bird

Step-by-step explanation:

8 0

2 years ago