Find the sum of a finite arithmetic sequence from n=1 to n=5 using the expression -3(4)^n-1

Answers

Answer 1

Answer:

Step-by-step explanation:

Arithmetic sequaence:

[tex]\sf a_n = -3(4)^n - 1\\\\a_1=-3*4^1 -1\\\\ = -3*4 - 1\\\\ = -12 - 1\\\\a_1=-13[/tex]

[tex]a_2 = -3*4^2-1\\[/tex]

    = -3*16 -1

     = -48 - 1

    = -49

difference = second term - first term

                 = -49 -(-13)

                = -49 + 13

             d = -36

[tex]\boxed{S_n=\dfrac{n}{2}[2a + (n-1)d]}[/tex]

[tex]\sf S_5=\dfrac{5}{2}*[2*(-13} + 4*(-36)]\\\\ =\dfrac{5}{2}[-26-144]\\\\=\dfrac{5}{2}*(-270)[/tex]

= 5*(-135)

= -675


Related Questions

What fraction is equivalent to six tenths and has a denominator of 100?

Answers

Answer:

6 = 6/10

Step-by-step explanation:

.6 = 6/10 , by definition. = 3/5 (reduced -- divide numerator and denominator by 2.

Answer:

[tex]\dfrac{60}{100}[/tex]

Step-by-step explanation:

Six tenths:

[tex]\dfrac{6}{10}[/tex]

where 6 is the numerator and 10 is the denominator

We want the denominator to be 100, so how do we convert 10 into 100?

We multiply by 10, since 10 x 10 = 100

When working out equivalent fractions, we must remember to do the same operation to both the numerator and denominator.  Therefore, we should multiply both by 10:

[tex]\dfrac{6 \times 10}{10 \times 10}=\dfrac{60}{100}[/tex]

Therefore, the fraction that is equivalent to six tenths and has a denominator of 100 is:

[tex]\dfrac{60}{100}[/tex]

(sixty hundredths)

Consider the expression 1.1(1.3)x+4Which of the following is an equivalent expression?

Answers

Answer:

the equivalent expression is 1.1(1.3)^4 ×(1.3)^x

Answer:

d

Step-by-step explanation:

i took the test

-
Using the GCF factor the given expression 4m - 20
4(m - 5)
2(2m - 10)
4m - 20)
2(2m - 20)

Answers

Hey there!

Finding something that’s equivalent to: 4m - 20


Option A.
4(m - 5)

= 4(m) + 4(-5)

= 4m - 20

Possibly Option A. is your answer.

Option B.
2(2m - 10)

= 2(2m) + 2(-10)

= 4m - 20

Possibly Option B. could be your answer


Option C.
4(m - 20)

= 4(m) + 4(-20)

= 4m - 80

Optipn C. isn’t your answer


Option D.
2(2m - 20)

= 2(2m) + 2(-20)

= 4m - 40

Option D. also isn’t your answer just like Option C.

FACTORS OF: 4m - 20

4: 1,2,4, & m

20: 1,2,4,5,10,& 20


LIKE TERMS: 1,2,4


GCF: 4


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

Two students each write a function, C(n), that they think can be used to find the number of circles needed to make the nth figure in the pattern shown.

Use the drop-down menus to explain why each function does or does not represent the number of circles needed to make the nth figure in the pattern.

Answers

The function that can be find used to find the number of circles needed to make the nth figure in the sequence is (C + 1) + 4.

How to calculate the sequence?

The sequence can be illustrated through the function (C + 1) + 4 where C is the previous number. For the third picture, the number of circles will be:

= (C + 1) + 4

= 5 + 4

= 9

The fourth term will be:

= 9 + 4

= 13

Therefore, each figure uses 4 circles more than the previous one.

Learn more about sequence on:

https://brainly.com/question/6561461

Answer:

Step-by-step explanation: This function can be used to find the number of circles needed to make the nth figure in the pattern.

Each figure uses 4 more circle(s) than the previous figure because an additional circle is added to the top, bottom, left, and right sides.

the other half i got incorrect.

Andrew drinks 1.9 litres of water each day for three years. By rounding the amount of water an the number of days to one significant figure find the approximate amount of water he drinks during the three years. [One year = 365 or 366 days]

Answers

Answer:

2081days or 2086days

Step-by-step explanation:

1.9(365)=693.5

1.9(366)=695.4

693.5(3)=2080.5

695.4(3)=2086.2

(2x+3)+(5x17)+90=180

Answers

Answer:

x=10

Step-by-step explanation:

Answer:

x is 10 degrees

Step-by-step explanation:

180-90=90

(2x+3)+(5x+17) = 90

7x+20=90

7x=70

x=10

Can you guys work it out

Answers

Answer:

x ≤ 45

Step-by-step explanation:

x + 35 ≤ 80

  - 35    -35

x ≤ 45

I hope this helps!

Hello!

Let's solve this inequality.

x+35≤80

Subtract 35 from both sides:

x≤80-35

x≤45

It means "less than or equal to"

So all numbers less than or equal to will make this inequality true.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

which number is equivalent to 5√8 x 3√4

A. 15√2

B. 60√2

C. 30√3

D. 60√3​

Answers

Answer:

B

Step-by-step explanation:

5×sqrt(8)×3×sqrt(4) = 15×sqrt(8)×sqrt(4) = 15×sqrt(8)×2 =

= 30×sqrt(8) = 30×sqrt(4×2) =

= 30×2×sqrt(2) = 60×sqrt(2)

A square is drawn below. What is value of x

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The opposite sides of a square are parallel, therefore the given angles are equal by ( Alternate interior Angle pair )

[tex]\qquad \sf  \dashrightarrow \:4x + 5 = 2x + 25[/tex]

[tex]\qquad \sf  \dashrightarrow \:4x - 2x = 25 - 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:2x = 20[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 10[/tex]

Hence, correct choice is B

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Order the numbers from least to greatest. −34, 0.5, 23,−73, 1.2 The order of the numbers from least to greatest

Answers

Answer:

-73, -34, 0.5, 1.2, 23

Step-by-step explanation:

Hope this helps:)....if not sorry for wasting your time and may God bless you:)

-73, -34, 0.5, 1.2, 23

Can someone please help me

Answers

(x-2)(2x+1)
On the x-axis y=0
x-2 = 0 or 2x + 1 = 0
x= 2 or 2x = -1
x= 2 or x = -1/2
Therefore the intercepts are
(2,0) and (-1/2 , 0)

Answer : 2nd Option

the volume of this is cone 923.16 cm what is the radius of this cone

Answers

Hey there!

[tex] \rightarrow \sf{ r = \sqrt{3 \frac{v}{\pi \ h} }} \: \rm{or} \: \sf{v = \frac{1}{3} \pi \: {r}^{2} \times h}[/tex]

[tex] \rightarrow \sf{923.16 = \frac{1}{3} (3.14) {r}^{2} \times h}[/tex]

[tex] \rightarrow \sf{\: 1.046667 {hr}^{2} =923.16}[/tex]

[tex] \rightarrow \sf{ \frac{1.046667 {hr}^{2} }{1.046667} = \frac{923.16}{1.046667} }[/tex]

[tex] \rightarrow \: \sf{ {r}^{2} = \frac{923.16}{1.046667h}}[/tex]

[tex] \rightarrow \: \sf{ r = \sqrt{ \frac{923.16}{1.046667h}}}[/tex]

A cat weighs​8 1/4​pounds.

How many ounces does the cat weigh?

Answers

The answer is C 132oz

Answer:

132 ounces

Step-by-step explanation:

1 pound = 16 ounces

8 1/4 x 16 = 132

Is the data Jamaya collected a random sample if the population is books from her entire household? Why or why not? *Remember that Jamaya picked 15 books from her book shelf in her bedroom.

Answers

Using sampling concepts, it is found that it is not a random sample, as it considers only the books in her bedroom, hence books from other people in the household are likely to not be considered.

What is sampling?

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which has to involve all groups in the population.

In this problem, a random sample should involve the books of all people in the household, not only Jamaya's. Hence, it is not a random sample, as it considers only the books in her bedroom, hence books from other people in the household are likely to not be considered.

More can be learned about sampling concepts at https://brainly.com/question/25122507

A coin is flipped 8 times. Find the probability of the event:
exactly 6 heads
A.0.4375
B.0.75
C.0.0039
D.0.109

Answers

b. 0.75 because if you flip it 8 times and get heads 6 times, the probability would be 6/8 and that would simplify to 3/4 (0.75).

Answer:

D. 0.109

Step-by-step explanation:

Just did the test, its not B

Can someone help me out? I can't understand this shape. (Explanation also please). I'll mark brainliest

Answers

The surface area of the rectangular prism is 46m²

How to find surface area of a rectangular prism?

length = 4mwidth = 2.5mheight = 2m

Surface area of a rectangular prism = 2(width×length + height×length + height×width)

SA = 2(wl + hl + hw)

= 2(2.5×4 + 2×4 + 2×2.5)

= 2(10 + 8 + 5)

= 2(23)

= 46m²

Therefore, the surface area of a rectangular prism is 46m²

Learn more about surface area:

https://brainly.com/question/16519513

I need help with this question 80 pts

Answers

Answer:

65

Step-by-step explanation:

angle 2 is equal to angle 4, so that means angle 4 is also 130⁰.

130=2y

130/2=2y/2

65=y

Answer:

y = 65°

Step-by-step explanation:

Vertical Angle Theorem:  When two straight lines intersect, the opposite vertical angles are always equal (congruent) to each other.

⇒ m∠2 = m∠4

⇒ 130° = 2y

⇒ y = 130° ÷ 2

⇒ y = 65°

Help Please Quick! Pleasee

Answers

Answer:

you can search them up! Just search up fractions calculator

Step-by-step explanation:

Help help help help help hel

Answers

Answer:

12

Step-by-step explanation:

P = 8

Q = 16

The value of PQ = 16 - 8 = 8

Since M is the midpoint of PQ,

PM = MQ

PM + MQ = PQ

PM + PM = PQ

2 PM = 8

PM = 8 / 2

PM = 4

The value of M

= 8 + 4

= 12

Answer:

M = 12

Step-by-step explanation:

If you want to find the midpoint between the numbers 8 and 16, follow the simple steps below.

First, add the two numbers: 8 + 16 = 24

Secondly, divide the total by 2: 24/2 = 12

The midpoint between 8 and 16 is 12.

hope this helps!! p.s. i really need brainliest :)

Complete the net worth statement. What is the net worth of the individual?
A) $171,645
B) $19,950
C) $21,000
D) $26,595

Answers

Considering it's concept, it is found that the net worth of the individual is given by:

D) $26,595.

What is the net worth of an individual?

It is given by the sum of the individual assets subtracted by the sum of it's liabilities.

Researching the problem on the internet, we have that:

The sum of the assets, in dollars, is of 545 + 165000 + 6100 = 171645.The sum of the liabilities, in dollars, is of 144000 + 1050 = 145050.

Hence, his net worth is given by:

N = 171645 - 145050 = $26,595.

More can be learned about net worth at https://brainly.com/question/12371230

The net worth of the individual with assets worth $171,645 and liabilities of $145,050 is D) $26,595.

What is the net worth?

The net worth is the value of assets less the value of liabilities.

The net worth shows the amount by which the assets have increased or decreased in value versus the liabilities.

Data and Calculations:

Assets = $171,645

Liabilities = $145,050
Net worth = $26,595 ($171,645 - $145,050)

Thus, the net worth of the individual with assets worth $171,645 and liabilities of $145,050 is D) $26,595.

Learn more about net worth at https://brainly.com/question/12371230

What is the solution to this system of
equations?
6x - 2y = 8
1-3x + y = -4
A. No Solution
B. (0, -4)
C. Infinite Solutions

Answers

Answer:

No solution

Step-by-step explanation:

System of Linear Equations given :

[1]           6x-2y=8

 [2]           1-3x+y=-4

Equations Simplified or Rearranged :

  [1]    6x - 2y = 8

  [2]    -3x + y = -5

Solve by Substitution :

// Solve equation [2] for the variable  y

 [2]    y = 3x - 5

// Plug this in for variable  y  in equation [1]

  [1]    6x - 2•(3x-5) = 8

  [1]    0 = -2 =>  NO solution

the product of two consecutive odd number is 143 find those two odd numbers show ll workings

Answers

Answer:

11,13

11×13=143

Step-by-step explanation:

please mark me as brainlest

The graph displays a linear function.

Answers

Answer:

[tex]y = -\frac{2}{3}x +0[/tex]  OR [tex]y = -\frac{2}{3}x[/tex]

Step-by-step explanation:

First, find the slope (m) using two points (0,0) and (-6, 4)

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{4-0}{-6-0} \\\\m=\frac{4}{-6}\\\\m=\frac{2}{-3}\\\\m=-\frac{2}{3}[/tex]

[tex]y=mx+b[/tex]

[tex]y = -\frac{2}{3}x +b[/tex]

Now, we find b using (-6, 4)

[tex]y = -\frac{2}{3}x +b[/tex]

[tex]4 = -\frac{2}{3}(-6) +b\\\\4 = \frac{12}{3} +b\\\\4 = 4 +b\\\\-4 -4\\\\0=b[/tex]

[tex]y = -\frac{2}{3}x +0[/tex]  OR [tex]y = -\frac{2}{3}x[/tex]

Hope this helps!

PLEASE HELP WILL MARK BRAINLIEST THANK YOU

Answers

Here is the answer: x=4

What fraction is equivalent to six tenths and has a denominator of 100?

Answers

Answer:

3/5

Step-by-step explanation:

3/5=6/10

3/5=60/100

Calculate the perimeter of the semi-circle below. Use 3.14 to approximate π.



12 cm

Answers

37.902

Step-by-step explanation:

3.14x12+12

This trapezoid represents the base of a right prism that has a surface area of 1280 square feet. The sum of the lengths of the legs of the trapezoid is 52 feet. What is the height of the prism? Enter your answer in the box.

Answers

Answer:

El area del trapecio mresponde a la relación

                      A = 1/2(B + b)*h

                          B = base mayor

                           b = bas menor

                           h = altura

En el caso en esrudio

                                              250 = 1/2(B + 20)*10

                                     2*250/10 = B + 20

                                                50 = B + 20

                                        50 - 20 = B

                                                  B = 30

                                                                BASE MAYOR = 30 PIES

What is the horizontal distance from the origin to the point (1,4)

Answers

Answer:

given ,

a point , let's say , A( 1 , 4 ) on the cartesion plane.

to find - the horizontal distance of the point from the origin.

[tex]\underline\bold{using \: Distance \: formula \:} \\ \\ d(AO) = \sqrt{( x_{2} - x_{1}) {}^{2} +( y_{2} - y_{1}) {}^{2} } \\ \\ d(AO) = \sqrt{(1 - 0) {}^{2} + (4 - 0) {}^{2} } \\ \\ d(AO) = \sqrt{1 + 4} \\ \\ d(AO) = \sqrt{5} units [/tex]

hope helpful :D

What's the value of X in the figure


145 (degrees) X (2x + 15)

Answers

Answer:

x=65°

Step-by-step explanation:

2x + 15= 145

2x+15-15=145-15  (Subtract)

2x=130 (Simplify)

2x/2=130/2 (Divide)

x=65 ← (Answer)

^^

。☆✼★━━━━━ ( ~ ) ━━━━━━━★✼☆。

help The area of a square

Answers

Answer:

[tex]2551\dfrac{1}{2}[/tex]

Step-by-step explanation:

[tex]\bf l = 20\dfrac{\sf 1}{4} \ in = \dfrac{81}{4} \ in[/tex]

[tex]\bf w = 10\dfrac{1}{2} = \dfrac{21}{2} \ in\\\\\\h = 12 \ in[/tex]

Volume of rectangular prism = l*w*h

                                                 [tex]= \dfrac{81}{4}*\dfrac{21}{2}*12\\\\\\= 81 *\dfrac{21}{2}*3\\\\\\= \dfrac{5103}{2}\\\\\\= 2551 \dfrac{1}{2} \ cubic \ inches[/tex]

Answer:

[tex]\sf 2551\frac12 \ cubic \ inches[/tex]

Step-by-step explanation:

volume of a cuboid = width × length × height

Given:

[tex]\sf width=10\frac12 \ in[/tex][tex]\sf length=20\frac14 \ in[/tex][tex]\sf height=12 \ in[/tex]

Substituting given values into the formula for volume:

[tex]\sf \implies volume=10\frac12 \times 20\frac14 \times 12[/tex]

                  [tex]\sf =\dfrac{21}{2} \times \dfrac{81}{4} \times \dfrac{12}{1}[/tex]

                  [tex]\sf =\dfrac{21 \times 81 \times 12}{2 \times 4 \times 1}[/tex]

                  [tex]\sf =\dfrac{20412}{8}[/tex]

                  [tex]\sf =2551\frac12 \ in^3[/tex]

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