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MatroZZZ [7]
3 years ago
12

Find the 9th term 1, 3/2, 9/4

Mathematics
1 answer:
Pie3 years ago
3 0

Answer:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by

2

3

2

3

gives the next term. In other words,

a

n

=

a

1

⋅

r

n

−

1

a

n

=

a

1

⋅

r

n

-

1

.

Geometric Sequence:

r

=

2

3

r

=

2

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

a

n

=

a

1

r

n

-

1

Substitute in the values of

a

1

=

1

2

a

1

=

1

2

and

r

=

2

3

r

=

2

3

.

a

n

=

(

1

2

)

⋅

(

2

3

)

n

−

1

a

n

=

(

1

2

)

⋅

(

2

3

)

n

-

1

Apply the product rule to

2

3

2

3

.

a

n

=

1

2

⋅

2

n

−

1

3

n

−

1

a

n

=

1

2

⋅

2

n

-

1

3

n

-

1

Multiply

1

2

1

2

and

2

n

−

1

3

n

−

1

2

n

-

1

3

n

-

1

.

a

n

=

2

n

−

1

2

⋅

3

n

−

1

a

n

=

2

n

-

1

2

⋅

3

n

-

1

Cancel the common factor of

2

n

−

1

2

n

-

1

and

2

2

.

Tap for more steps...

a

n

=

2

n

−

2

3

n

−

1

a

n

=

2

n

-

2

3

n

-

1

Substitute in the value of

n

n

to find the

n

n

th term.

a

5

=

2

(

5

)

−

2

3

(

5

)

−

1

a

5

=

2

(

5

)

-

2

3

(

5

)

-

1

Simplify the numerator.

Tap for more steps...

a

5

=

8

3

(

5

)

−

1

a

5

=

8

3

(

5

)

-

1

Simplify the denominator.

Tap for more steps...

a

5

=

8

81

a

5

=

8

81

Step-by-step explanation:

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guajiro [1.7K]

Answer:

Part 1) y=-\frac{1}{5}x-1

Part 2) y=3x-16

Part 3) y=4

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

Part 1) we have

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<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute

m=\frac{-2+3}{5-10}

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we have

m=-\frac{1}{5}

point (10,-3)

substitute in the equation y=mx+b  and solve for b

-3=-\frac{1}{5}(10)+b

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substitute

y=-\frac{1}{5}x-1

Part 2) we have

(6,2) (7,5)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute

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m=\frac{3}{1}

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<em>Find the value of b</em>

we have

m=3

point (6,2)

substitute in the equation y=mx+b  and solve for b

2=3(6)+b

2=18+b

b=2-18=-16

substitute

y=3x-16

Part 3) we have

(4,4) (-7,4)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute

m=\frac{4-4}{-7-4}

m=\frac{0}{-11}

m=0

This is a horizontal line (parallel to the x-axis)

The y-intercept b is equal to the y-coordinate

<em>therefore</em>

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Wo similar triangles are shown on the coordinate grid:
anygoal [31]

Answer:

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8 0
3 years ago
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Komok [63]

repeating fraction, nice

2.16161616...=2+0.16161616...
solve the repeating part
let's say x=0.16161616
2 places repeat, multiply x by 10^2 or 100
100x=16.161616

now subtract x from taht
100x-x=16.161616-0.16161616
the repeats cancel and we get
99x=16
divide both sides b 99
x=16/99

so
16/99=0.16161616...

2+16/99 is the fraction
if ya wanted 1 fraction then
2+16/99=
198/99+16/99=
214/99

2.161616=214/99
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hodyreva [135]
If you simplify (take out the brackets) of this equation. 5(x+10)=30 then it would be

5 times x + 5 times 10 = 30

5x+10=30

So yes they have the same solution

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Why would the law of cosines be used to solve for b in the triangle below? SAS is given, and the unknown measure, b, is a side l
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Answer:

it's a

Step-by-step explanation:

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