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inessss [21]
3 years ago
10

What is the seventh term of a sequence whose first term is 1 and whose common ratio is 3?

Mathematics
1 answer:
ikadub [295]3 years ago
7 0
\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}\\
----------\\
a_1=1\\
r=3\\
n=7
\end{cases}
\\\\\\
a_7=1\cdot 3^{7-1}\implies a_7=1\cdot 3^6\implies a_7=1\cdot 729\implies a_7=729
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Answer:

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<em><u>Or ;</u></em>

{( \sqrt{ {x}^{ - 3} } )}^{5}  =  {( \sqrt{ \frac{1}{ {x}^{3} }} })^{5}  = ( { \frac{ \sqrt{1} }{ \sqrt{ {x}^{3} } } })^{5}  \\  \\  =  ( { \frac{1}{ \sqrt{x}  \sqrt{ {x}^{2} } } })^{5}  =  ({ \frac{1}{ x\sqrt{x} }})^{5}   \\  \\  = ( \frac{ {(1)}^{5} }{ {x}^{5} ( \sqrt{x} )^{5} } ) =  \frac{1}{ {x}^{5}  \times  {x}^{ \frac{1}{2} \times 5 } }  \\  \\  =  \frac{1}{ {x}^{5}  \times  {x}^{ \frac{5}{2} } }  =  \frac{1}{ {x}^{5}  \sqrt{ {x}^{5} } }  \\  \\  =  \frac{1}{ {x}^{5} \sqrt{ {x}^{4} {x}^{1}  }  }  =  \frac{1}{ {x}^{5}  \sqrt{x}  \sqrt{( { {x}^{2} })^{2} } }  \\  \\  =  \frac{1}{ {x}^{5} {x}^{2}  \sqrt{x}  }  =  \frac{1}{ {x}^{7} \sqrt{x}  }   =  \frac{ \sqrt{x} }{ {x}^{8} }

3 0
2 years ago
The graph displays the function g(x) = 2 cos(x+)-2.
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Answer:

Area of a triangle is :

it's given that ;

base = 10 m

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Therefore, the area of triangle is 80 m²

Step-by-step explanation:

3 0
2 years ago
A standard basketball court is a rectangle with the length 94 feet and width 50 feet. How much square feet or flooring would you
Lapatulllka [165]

Answer:

4700 ft

Step-by-step explanation:

Find the area (l x w)

94 x 50 = 4700 feet

DON'T FORGET UNITS

3 0
3 years ago
Read 2 more answers
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stira [4]

Answer:

$8.85

Step-by-step explanation:

This a question of direct variation, so we can make out a relationship between the two factors. 12 is 2/3 of 18, so the cost of 12 would also be 2/3 of the cost of 18. We can now make an equation to solve.

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6 0
3 years ago
Ryan is remodeling his kitchen floor, which is 110 square feet. He used
irakobra [83]

Answer:

He will need 9 tiles

Step-by-step explanation:

Step one:

let us highlight the given parameters

Given data

the size of the kitchen floor is 110 ft^2

the size of the bathroom is 28 ft^2

he used 32.5 tiles for the kitchen

and used x tiles for the bathroom

Step two:

if he used 32 tiles for 110 ft^2 kitchen

he will use x tiles for 28 ft^2 bathroom

cross multiplying we have

x= (32*28)/110

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x= 8.145

<em>Approximately he will need 9 tiles</em>

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