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Maksim231197 [3]
3 years ago
6

What is the summation notation for the geometric series 5 + 10 + 20 + 40 + 80?

Mathematics
2 answers:
katrin [286]3 years ago
8 0
S_{5}=\sum\limits_{k=1}^{5}{5\cdot 2^{k-1}}
Gekata [30.6K]3 years ago
3 0
Anyhow, the common ratio is 2, and the first term is 5 and since there are 5 terms, n = 5,

\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}\\
----------\\
a_1=5\\
n=5\\
r=2
\end{cases}
\\\\\\
\sum\limits_{i=1}^{5}~5\cdot 2^{i-1}
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Please help, I've been working on this for 30 min now...
MaRussiya [10]

Step 1: Y is equal to \frac{3}{4}x + 2 so where ever you see a y in the equation 3x - 4y = -5 replace it with \frac{3}{4}x + 2

3x - 4(\frac{3}{4}x + 2) = -5

Now all your variables are x and you can solve for x

Step 2: Distribute for to the numbers in the parentheses

3x - 3x - 8 = -5

Step 3: Combine like terms

0x - 8 = -5

0x = 3

Step 4: Isolate x

0x/0 = 3/0

3/0 is undefined

^^^ This means that there is no answer

If you look at the graph below you can see that these lines are parallel and therefore have no intersection point

Hope this helped!

3 0
3 years ago
Put the following equation of a line into slope-intercept form, simplifying all fractions 6x+4y=4
s344n2d4d5 [400]

Answer:

y=-\frac{6}{4}x+1

Step-by-step explanation:

6x+4y=4

4y=4-6x

y=1-\frac{6}{4}x

y=-\frac{6}{4}x+1

6 0
2 years ago
According to Okun's law, if the unemployment rate goes from 7% to 4%, what
tatyana61 [14]

Answer:

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
For Sophia's graduation party, several tables of the same width will be arranged end to end to form a serving table with a
madreJ [45]

Answer:

Width=4.7 ft

Length=16.1 ft

Step-by-step explanation:

Let the width of the table to be x ft

Then the length should be two more than three times the width= 2+3x ft

The area of the serving table should be 75 ft²

But you know the area of this table is calculated by multiplying the length by the width of the table

Hence, Area= length× width

Length=x ft  and width =2+3x ft

75ft²= (x ft) × (2+3x ft)

75=x*(2+3x)\\\\75=2x+3x^2\\\\3x^2+2x-75=0

Apply the quadratic formula to solve this quadratic equation

The formula is ;

x= (-b ±√b²-4ac)÷2ac

where a=3, b=2 and c=-75

x= (-2 ± √2²-4×3×-75)÷(2×3)

x=(-2±√4+900)÷6

x=(-2±√904)÷6

x=(-2±30.1)÷6

x=(-2+30.1)÷6=4.683⇒4.7(nearest tenth)

or

x=(-2-30.1)÷6= -32.1÷6=-5.35⇒ -5.4

Taking the positive value

x=width =4.7 ft

2+3x= length= 2+3(4.7)=16.1 ft

6 0
4 years ago
Which system of equations represents the matrix shown below? See picture
algol [13]
Answer to this question is B
6 0
3 years ago
Read 2 more answers
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