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3 years ago

Find the sum of the series 9+3+1+........+1/27

Mathematics

1 answer:

Elina [12.6K]3 years ago

4 0

Answer:

364/27

Step-by-step explanation:

9, 3, 1, ... is a geometric sequence with common ratio r = 1/3.

The nth term is a1rn-1.

If a1rn-1 = 1/27, then 9(1/3)n-1 = 1/27

32(3-1)n-1 = 3-3

3231-n = 3-3

33-n = 3-3

3-n = -3

n = 6

The sum, Sn, of the first n terms of a geometric sequence is given by Sn = a1(1 - rn) / (1 - r).

So, 9 + 3 + 1 + ... + 1/27 = S6 = 9(1 - (1/3)6) / (1 - 1/3)

= 9(1 - 1/729) / (2/3)

= (27/2)(728/729) = 364/27

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Ainat [17]

Answer:

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mr Goodwill [35]

Answer:

f(x) = (x - (-5))^2 + (-18)

Step-by-step explanation:

Given:

f(x) = x^2 + 10x + 7

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f(x) = ax^2 + bx + c is a quadratic function.

The vertex form of f(x) is a(x - h)^2 + k, where (h, k) is the vertex.

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3 years ago

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Vesnalui [34]

Answer:

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2 years ago

2 easy math questions!!!!!! Show work! Multiple choice!

elena55 [62]

Greetings!

<u>Question Seven:</u>
To find the slope given two points, we can use the slope formula:
$m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Input the points: (-11,5) (-6,1)
$m= \frac{1-5}{-6-(-11)}$

Simplify the equation:
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A parallel slope would be identical to this slope.

Therefore, the answer is B:
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<u>Question Eight:</u>
This question essentially asks you to rearrange the equation into slope y-intercept form:
$y=mx+b$

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Therefore the answer is F:
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I hope this helped!
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Georgia [21]

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