Type the missing number that makes these fractions equal: 4/?=8/14

Mathematics

2 answers:

ozzi3 years ago

7 0

Answer:

4/7 = 8/14

Step-by-step explanation:

Nataly_w [17]3 years ago

6 0

Answer:

Step-by-step explanation:

$\frac{4}{x} =\frac{8}{14} \\$

cross multiply

8x = 14 x 4

8x = 56

x = 7

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What is the sum of the geometric series:

I am Lyosha [343]

by looking at the expression, we can pretty much see who's the common factor and first term.

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}
\end{cases}
\\\\[-0.35em]
\rule{34em}{0.25pt}$

$\bf \sum\limits_{n=1}^{4}~(\stackrel{\stackrel{a_1}{\downarrow }}{-2})(\stackrel{\stackrel{r}{\downarrow }}{-3})^{n-1}\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\[-0.5em]
\hrulefill\\
a_1=-2\\
r=-3\\
n=4
\end{cases}
\\\\\\
S_4=-2\left( \cfrac{1-(-3)^4}{1-(-3)} \right)\implies S_4=-2\left( \cfrac{1-81}{1+3} \right)
\\\\\\
S_4=-2\cdot \cfrac{-80}{4}\implies S_4=-\cfrac{-80}{2}\implies S_4=40$