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3 years ago

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

1 answer:

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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Pls solve this question

just olya [345]

Answer:

${( \sqrt{ {x}^{ - 3} }) }^{5} = ({( {x}^{ - 3}) }^{ \frac{1}{2} } ) ^{5} \\ \\ = {x}^{ - 3 \times \frac{1}{2} \times 5} = {x}^{ - \frac{15}{2} } = \frac{1}{ {x}^{ \frac{15}{2} } }$

Or ;

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

3 0

2 years ago

The graph displays the function g(x) = 2 cos(x+)-2.

Talja [164]

Answer:

Area of a triangle is :

it's given that ;

base = 10 m

height = 16 cm

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

A 12- pack of 8- ounce juice boxes costs $5.90. How much would an 18- pack of the same 8- ounce juice boxes cost?

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.

$\frac{2}{3} x=5.9\\2x=17.7\\x=8.85$

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

x= 896/110

x= 8.145

Approximately he will need 9 tiles

4 0

3 years ago