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JulsSmile [24]
3 years ago
11

What is the nth term of the geometric sequence that has a common ratio of 6 and 24 as it’s third term?

Mathematics
1 answer:
Llana [10]3 years ago
8 0
\bf \begin{array}{ccll}
n&term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
1&a_1&a_1\\
2&a_2&6a_1\\
3&a_3&6(6a_1)\\
&&36a_1
\end{array}\implies \stackrel{\textit{3rd term is 24}}{36a_1=24}
\\\\\\
a_1=\cfrac{24}{36}\implies  a_1=\cfrac{2}{3}

\bf n^{th}\textit{ term of a geometric sequence}
\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=6\\
a_1=\frac{2}{3}
\end{cases}
\\\\\\
\boxed{a_n=\cfrac{2}{3}\cdot 6^{n-1}}
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Answers:

1) The dependent variable is the boiling point of water and the independent variable is the altitude.

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Explanation:

1) given

Table:

<span>Altitude (in thousands of feet)    Boiling Point of Water (Fahrenheit)

(sea level) 0                                212
0.5                                               211.1
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2.0                                               208.4
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4.0                                               204.8
4.5                                               203.9

2) The independent variable is the input of the function, and the dependent variable is the output of the function.

The input determines the output once the rule is established.

Therefore:

a) the independent variable is the altitude, and
b) the dependent variable is the boiling point of water in Farenheit.

3) The slope of the graph would be:

                 change in the dependent variable          change in boiling point
slope = --------------------------------------------------- =  ---------------------------------
</span>                 change in the independent variable          change in altitude

Therefore, the slope represents the average change in the boiling boilin point of water every one thousand feet on change of altitude.

If the relationship is not linear, then the slope is not constant, and you will have different slopes for different parts.

If the slope is negative, means that as the altitude increase the boiling point of water decrease.

You can calculate the slope using any two pair of points (data)

              212 - 210           2
slope =---------------- =   ------- = - 2
                0 - 1            - 1

or, using other pair of points:

                204.8 - 210           -5.2             
slope = --------------------- =   --------- = -2.6
                  4.0 - 2.0               2.0

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when x =7.5, the equation will be y=5(7.5). So y=37.5

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