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3 years ago

PLEASE HELP ILL VOTE

Mathematics

2 answers:

docker41 [41]3 years ago

5 0

Answer:

213

Step-by-step explanation:

Ksju [112]3 years ago

3 0

Answer:

213

Step-by-step explanation:

213

123

21312

3213

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Find the sum of the geometric series 512+256+ . . .+4

mario62 [17]

$\bf 512~~,~~\stackrel{512\cdot \frac{1}{2}}{256}~~,~~...4$

so, as you can see above, the common ratio r = 1/2, now, what term is +4 anyway?

$\bf n^{th}\textit{ term of a geometric sequence}\\\\a_n=a_1\cdot r^{n-1}\qquad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\a_n=+4\end{cases}$

$\bf 4=512\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{4}{512}=\left( \cfrac{1}{2} \right)^{n-1}\\\\\\\cfrac{1}{128}=\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{1}{2^7}=\left( \cfrac{1}{2} \right)^{n-1}\implies 2^{-7}=\left( 2^{-1}\right)^{n-1}\\\\\\(2^{-1})^7=(2^{-1})^{n-1}\implies 7=n-1\implies \boxed{8=n}$

so is the 8th term, then, let's find the Sum of the first 8 terms.

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\n=8\end{cases}$

$\bf S_8=512\left[ \cfrac{1-\left( \frac{1}{2} \right)^8}{1-\frac{1}{2}} \right]\implies S_8=512\left(\cfrac{1-\frac{1}{256}}{\frac{1}{2}} \right)\implies S_8=512\left(\cfrac{\frac{255}{256}}{\frac{1}{2}} \right)\\\\\\S_8=512\cdot \cfrac{255}{128}\implies S_8=1020$

7 0

4 years ago

If 160,000÷n=4 then what is n?

shusha [124]

160,000/4 = n
n = 40,000

Answer: n = 40,000

8 0

3 years ago

Read 2 more answers

During the first week of a summer camp 2 out of 3 campers were boys. During the second week 3 out of 5 were boys. There were a 1

rewona [7]

Step-by-step explanation:

2/3=10/15 (divide 15 by 3 to get 5, then multiply both numerator and denominator by 5 to set equivalent)

3/5=9/15

10/15 is greater than 9/15, so during the 1st week there were more boy campers

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3 years ago

14^(5x+2) < 11^(4x-1)

kherson [118]

To simplify 14^(5x+2)<11(4x-1)
x < -2.130032

4 0

3 years ago

Write an equation in slope intercept form for a line that goes through the point (-9,4) and is perpendicular to line y=-3x-2

nadezda [96]

Answer:

y = 1/3x + 7

Step-by-step explanation:

Perpendicular slope is opposite reciprocal so it will be 1/3

Use the slope and point given and plug into y = mx + b

4 = 1/3 (-9) + b

4 = -3 + b

7 = b

write new equation with new b and m

y = 1/3x + 7

3 0

3 years ago