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balandron [24]
3 years ago
12

Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15

Mathematics
2 answers:
Thepotemich [5.8K]3 years ago
7 0

Answer:

the summation of 4 times negative 3 to the n minus 1 power, from n equals 4 to 15.

Step-by-step explanation:

goblinko [34]3 years ago
3 0
a_n=5 \ for \ n=1 \\
a_n=-10 \ for \ n=2 \\
a_n=20 \ for \ n=3

You can see it's a geometric sequence because the ratio is constant (\frac{a_3}{a_2}=\frac{a_2}{a_1}).
The nth term of a geometric sequence:
a_n=a_1 \times r^{n-1}

a_1=5 \\
r=\frac{a_2}{a_1}=\frac{-10}{5}=-2 \\ \\
a_n=5(-2)^{n-1}

It has to be the sum for term 4 through term 15, so n=4 and the number above the sigma is 15.

Your answer:
\sum^{15}_{n=4} 5(-2)^{n-1}
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james' daily wage was $5 more than Davis's. Although James worked 3 days less than David, they earned $180 each. Find the number
zalisa [80]

Answer: 9 days

Step-by-step explanation:

Let x represent James' daily wage

James' daily wage was $5 more than Davis's. It means that Davis's daily wage will be $(x-5)

Let y represent number of days that James worked. James worked 3 days less than David. It means that the number of days that Davis worked would be (y + 3) days

they earned $180 each. Total amount of money earned by either of of them is the product of wage and the number of days worked.

Since James earned $180, then

180 = xy - - - - - - - - 1

Since Davis also earned $180, then

180 = (x - 5)(y + 3)

xy +3x -5y -15 = 180 - - - - - - - - 2

Substituting xy = 180 into equation 2

It becomes

180 + 3x - 5y -15 = 180

3x - 5y = 180 - 180 + 15

3x - 5y = 15 - - - - - - -3

From equation 1, x = 180/y

Substituting x = 180/y into equation 3, it becomes

3 × 180/y - 5y = 15

540 - 5y^2 = 15y

5y^2 + 15y -540 = 0

Dividing through by 5

y^2 + 3y -108 = 0

y^2 + 12y - 9y -108 = 0

y(y + 12) - 9(y + 12) = 0

y + 12 = 0 or y - 9 = 0

y = -12 or y = 9

Since the number of days cannot be negative, then,

Number of days that James worked will be 9 days

8 0
3 years ago
5/2+18/5+11/4 what is the answer for this question​
Likurg_2 [28]

Answer:

Step-by-step explanation:

basicallyi you want to find a common denominator before you add them up. the common denominator in this case would be 20, since it's the first common multiple all of them share

50/20 plus 72/20 plus 55/20

177/20 would be your answer

3 0
3 years ago
Read 2 more answers
NEED RN, WORTH 20! <br> What is the value of x?
max2010maxim [7]

Answer:

x = 5.625

Step-by-step explanation:

<u>Step 1:  Make an expression</u>

<u />\frac{3}{4} = \frac{x}{7.5}

<u>Step 2:  Cross Multiply</u>

<u />\frac{3}{4} = \frac{x}{7.5}

4 * x = 7.5 * 3

4x = 22.5

<u>Step 3:  Divide both sides by 4</u>

<u />4x / 4 = 22.5 / 4

x = 5.625

Answer:  x = 5.625

5 0
3 years ago
Is a parallelogram always a square?<br> yes<br> no
polet [3.4K]

Answer:

yes

Step-by-step explanation:

4 0
3 years ago
Find two matrices A and B such that 2A-3B= [5 0
amm1812

The easy answer: If, say, B is the zero matrix, i.e.

B=\begin{bmatrix}0&0\\0&0\end{bmatrix}

then

2A=\begin{bmatrix}5&0\\-1&2\end{bmatrix}\implies A=\begin{bmatrix}\dfrac52&0\\\\-\dfrac12&1\end{bmatrix}

3 0
3 years ago
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