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4 years ago

What is the sum of a 7-term geometric series if the first term is 6, the last term is 24,576, and the common ratio is 4?

Mathematics

1 answer:

mash [69]4 years ago

6 0

Answer:

The sum is 32766.

Step-by-step explanation:

The 7 terms of the series are as follows:

$n_i = 6\cdot 4^i\,\,\,\mbox{for}\,\,\, i=0,1,...,6$

namely: 6, 24, 96, 384, 1536, 6144, 24576

and their sum is 32766.

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3 years ago

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At sea level, the pressure is 1013, that's when the altitude is at 0, sea level, let's see

$\bf \textit{Periodic Exponential Decay}\\\\
A=I(1 - r)^{\frac{t}{p}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &1013\\
I=\textit{initial amount}\\
r=rate\to 11.8\%\to \frac{11.8}{100}\to &0.118\\
t=\textit{meters climbed}\to &0\\
p=period\to &1000
\end{cases}
\\\\\\
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so, the inital amount is 1013, when t = 0,

$\bf \textit{Periodic Exponential Decay}\\\\
A=I(1- r)^{\frac{t}{p}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\to &1013\\
r=rate\to 11.8\%\to \frac{11.8}{100}\to &0.118\\
t=\textit{meters climbed}\to &t\\
p=period\to &1000
\end{cases}
\\\\\\
A=1013(1-0.118)^{\frac{t}{1000}}\implies A=1013(0.882)^{\frac{t}{1000}}$

now, to check the atmospheric pressure at 4000, simply set t = 4000, to get A.

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3 years ago