The fourth term of a geometric series is 10 and the seventh term of the series is 80. Find the sum to 10 terms of the series.

Answers

Answer 1

The geometric series with 4th term as 10 and 7th term as 80 has the sum of the first tenth terms as 1278.75.

How to find sum of terms in geometric series?

aₙ = arⁿ⁻¹

where

a = first termr = common ration = number of terms

Therefore,

10 = ar³

80 = ar⁶

Hence,

a = 10 / r³

80 = (10 / r₃) r⁶

80 = 10r³

r³ = 80 / 10

r = ∛8

r = 2

a = 10 / 2³

a = 10 / 8 = 5 / 4

The sum of 10 terms can be calculated as follows:

Sₙ = a(rⁿ - 1) / r - 1

Sₙ = 5 / 4 (2¹⁰ - 1) / 2 - 1

Sₙ = 5 / 4 (1024 - 1) / 1

Sₙ = 1.25(1023)

Sₙ = 1278.75

learn more on geometric series here: https://brainly.com/question/13592208


Related Questions

The roof of a tower in a castle is shaped like a cone. The height of the roof is 30 ft, and the radius of the base is 15 ft. What is the surface area of the roof?

Answers

Answer:

area=2πr

= 22/7*15

= 47.142

kassim has a money box containing 100 mixed sh 5 and sh 10 coins with a total value of sh 600. How many of each type of coin does the box contain

Answers

Answer

90

Step-by-step explanation

600 divided by 100

600 / 100 (5+10)

Which of the following expressions is equivalent to……

Answers

Answer:

Box 4

Step-by-step explanation:

negative divided by negative is positive so both negatives cancel out and u get (5/6) / (1/3)

please help
me answer this question

Answers

I hope I can help you:)

Answer:

x ≥ 4

Step-by-step explanation:

Given:

[tex]\displaystyle \large{3x-1\geq 11}[/tex]

Add both sides by 1:

[tex]\displaystyle \large{3x-1+1\geq 11+1}\\\displaystyle \large{3x\geq 12}[/tex]

Divide both sides by 3:

[tex]\displaystyle \large{\dfrac{3x}{3} \geq \dfrac{12}{3}}\\\displaystyle \large{x\geq 4}[/tex]

Hence, the solution is x ≥ 4

What is the volume of this cone? Use 3.14 for π and round your answer to the nearest tenth.

In your answer, give the volume of the cone rounded to the nearest tenth, and then explain how you calculated it.

Answers

Answer:

volume = 33.5 in³

Step-by-step explanation:

Formula:

[tex]\sf volume \ of \ a \ cone=\dfrac13\pi r^2h[/tex]

Given:

r = 2 inh = 8 inπ = 3.14

Substituting the given values into the formula:

[tex]\sf \implies volume=\dfrac13 \times 3.14 \times 2^2 \times 8[/tex]

                  [tex]=\dfrac13 \times 3.14 \times 4 \times 8[/tex]

                  [tex]\sf =33.49333333...[/tex]

                  [tex]\sf =33.5 \ in^3 \ (nearest \ tenth)[/tex]

-7/3y-2/9=1/3 solve for y

Answers

Answer:

y = -12

Step-by-step explanation:

-7/3y - 2/9 = 1/3

cross multiple for 1/3:

-21/3y - 6/9 = 1

cross multiply for 3y and 9:

-21 - 6 = 3y + 9

3y + 9 = -27

3y = -36

y = -12

1. Tom rides his bike 6_1/4 miles round trip to work. He works 2 days each
week. How far will Tom ride his bike to and from work in 5 weeks?
⚫️31_1/4 miles
⚫️62_1/2 miles
⚫️12_1/2 miles
⚫️62 miles

Answers

Answer:

B. 62 1/2

Step-by-step explanation:

how to express 1 cm as a fraction of 1 meter in decimal form

Answers

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

Let's see ~

Remember : value of 1 meter = 100 centimeters

[tex]\qquad \sf  \dashrightarrow \:1 \: m = 100 \: cm[/tex]

[tex]\qquad \sf  \dashrightarrow \:1 \: cm = \frac{1}{100} \: m[/tex]

[tex]\qquad \sf  \dashrightarrow \:1 \: cm = 0.01 \: m[/tex]

・ .━━━━━━━†━━━━━━━━━.・

As we know

100cm=1m

So

turn down to fraction

[tex]\\ \rm\rightarrowtail \dfrac{1}{100}[/tex]

Turn to decimal

[tex]\\ \rm\rightarrowtail 0.01m[/tex]

If x = 9 units , y = 3 units , and h= 11 units what is the area of the trapezoid

Answers

Hey there!

Your area of a trapezoid


a = a + b / 2(h)

area = base + base / 2(height)


YOUR EQUATION:

area = 9 + 3 / 2(11)

area = 12/2(11)

area = 6(11)

area = 66


Thus, your answer is probably: 66


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

the sum of three consecutive natural numbers is 1146, find the numbers.

the three numbers in increasing order are ______ , _____, and ________

Answers

[tex]\text{Let the 3 consecutive numbers be}~ x,~x+1~ \text{and} ~x+2.\\\\\text{According to the condition,}\\\\x+x+1+x+2 = 1146\\\\\implies 3x +3 = 1146\\\\\implies 3(x+1) = 1146\\\\\implies x+1 = \dfrac{1146}3 = 382\\\\\implies x= 382-1 = 381\\\\\text{Now, the numbers are}~ 381,~382~\text{and}~383[/tex]

You can run at a speed of 6 mph and swim at a speed of 3 mph and are located on the shore, 5 miles east of an island that is 1 mile north of the shoreline. How far (in mi) should you run west to minimize the time needed to reach the island

Answers

Answer:

I think I should run 5miles

Need additional math help 50 pts

Answers

Answer:

12

Step-by-step explanation:

This thing to know about this question is that angle 1 and angle 3 are actually the same.

When two lines intersect, the opposite angles such as that shown in 1 and 3 are equal to each other.

So what you can do is set angle 1 and 3 equal to each other like so:

5x+10 = 70

Then solve for x

5x+10 = 70

5x = 60

x = 12

The answer is 12.
Hope this helps

A closet contains 5 cases of laundry detergent. Each case contains 12 bottles. Each bottle contains 3 liters of detergent.

How many liters of laundry detergent in all are in the closet?

Answers

Each bottle in the case is 3 litres in capacity, we found the total number of bottles to be 60, hence the number of litres is 180 litres

Capacity of Items

Given Data

Number of Cases of Detergent = 5Number of Bottles on the closet = 5*12 = 60 bottles

Required : the total litres

If each bottle is 3 litres in capacity and we have 60 bottles

Then the total amount in litres is

= 60*3

= 180 litres

Learn more about capacity of items here

https://brainly.com/question/21036176

A spinner has 16 equal-sized sections. Twelve of the sections are orange.
a. What is the probability that the spinner will land on orange?
b. Use words to describe the probability
a.
out of 16, or
.
4
b. It is
that the spinner will land on orange.

Answers

The probability that the spinner will land on orange is the likelihhood of landing on orange

The probability that the spinner will land on orange is 0.75

How to determine the probability?

From the question, we have:

Spinner section = 16

Orange section = 12

So, the probability that the spinner will land on orange is:

p = 12/16

Evaluate

p = 0.75

Hence, the probability that the spinner will land on orange is 0.75

Read more about probability at:

https://brainly.com/question/251701

-1/4 (24ab + 8c) please help

Answers

Answer-6ab-2chope this helps! :)

15x + 2y /= 38
x >/= 0; y>/= 0

Answers

not so sure about the answer

Help picture below problem 15

Answers

Answer:

Supplementary

Step-by-step explanation:

The two angles are completely different from each other and if you combine them together it'll form a straight line making it 180 degrees

Determine the value of x if the mode is 18

Answers

Nobody can solve this without any further information?

1. Matthew is at the beach with his family. He is using a rectangular prism-shaped container to mold sand for his sandcastle. The container has the following dimensions: 12 in. by in. by in.

(a) Matthew noticed that the container was one-fourth full of sand. How many more cubic inches of sand would be required to fill the container? Show your work.

(b) Matthew’s father has a container that has dimensions that are each double the dimensions of Matthew’s container. Matthew thought that the volume would also double. Is Matthew correct? How many times greater is the volume of the larger container than the volume of the smaller one? Show your work and explain your reasoning.

2. Jasmine is making a 3-tiered wedding cake. The cake is made up of 3 rectangular prisms.
The bottom tier has a width of 16 in, a length of 16 in, and a height of in. The middle tier has the same height as the bottom tier but has a width and length that are each of the dimensions of the bottom tier. The top tier also has the same height as the bottom tier, but its width and length are each of the dimensions of the middle tier. Jasmine has made enough batter for 2,200 in3 of cake.
Does Jasmine have enough batter to make this cake? Explain and show your work.


3. A rectangular prism has dimensions of , 2, and in.
(a) Determine the edge length of the largest unit cube that you could use to pack the prism. Explain.
(b) What is the volume of the prism? Explain.
(c) How many cubes with the edge length from part (a) will fit into the prism? Explain.

HELPPP!!!ASAP!! K12 PLEASE PLEASE HELP!!!!!!

Answers

Answer:

e

Step-by-step explanation:

cus e duh

What is the length of the triangular prism shown? 25 cm
15 cm
9 cm
25 cm
12 cm the answers are A.86 B.1008 C.1350 D.1080

Answers

The length is 25cm and the surface area is 1008 cm.

To calculate surface area of an object you must calculate the area of each shape land then add them all together.

Answer:

Total Surface Area = 1008 cm^2

Step-by-step explanation:

2 X 1/2 X (12 X 9) (Surface area of the two triangles) (Area of triangle = 1/2 Base X Height)

+ 25 X 15 (Slanted Surface)

+ 25 X 9 (Back Rectangle)

+ 25 X 12 (Bottom Rectangle)

= 1008

awdawddwawwwwwwwwwwwwwwwd dwd awdw w ddw

Answers

Answer:

I'm sorry i dont think i understand what do u need help with

Step-by-step explanation:

Pls, Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

I can help you if you still!!!

Please help me ASAP

( I will mark brainliest )

Answers

e=10
give me brain list please

simplify the following 72÷6+3×2​

Answers

Answer:

18

Step-by-step explanation:

Use PEDMAS

In this, we have to do first division , then multiplication and finally addtion.

72 ÷ 6 + 3*2 = 12 + 3*2       {division is done}

                     = 12 + 6         {Multiplication is done}

                     = 18


g. a car travels at 60m/s for 50minutes
south west.calculate how far it will travel

Answers

Step-by-step explanation:

first we want to convert it to minutes so we multiply 60m/s by 60. 3600m/min or 3.6km/min

we just multiply 50 by 3.6.

therefore the car travels 180km south west

(3√7 +5)^2
simplify the problem to its simplest form.

Answers

Answer:

88 + 30[tex]\sqrt{7} \\[/tex]

Step-by-step explanation:

Expand to make easier:

(3[tex]\sqrt{7} \\[/tex] + 5) x (3[tex]\sqrt{7} \\[/tex] + 5)

FOIL:

9(7) + 15    [tex]\sqrt{7}[/tex] + 15[tex]\sqrt{7}[/tex] + 25

Simplify:

63 + 30[tex]\sqrt{7}[/tex] + 25

88 + 30[tex]\sqrt{7}[/tex]

The volume of a cylinder is 81 pi in^3 and the height of the cylinder is 1 in. What is the radius of the​ cylinder

Answers

Answer:

18/20π

Step-by-step explanation:

81π ÷ 1 = 81π

81π ÷2 = 18/20π

You do this because the radius is half of the diameter and you need to get rid of the hight by dividing it from the volume.

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax?

Answers

Answer:

2 toppings   need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same

Step-by-step explanation:

                   t=toppings

6.80 +0.90t = 7.30+0.65t

0.25t = 0.5

  t = 2

         

what is 7 times 3 fiths

Answers

Answer:

4-1.5 or 21/5 or 4.2

Step-by-step explanation:

Multiple: 7 * 3/5 = 7 · 3/1 · 5 = 21/5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(21, 5) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seven multiplied by three fifths = twenty-one fifths.

Frank is surveying shoppers about their use of the new food court in a mall. Which question in his survey is a statistical question?

How many hours do you spend at the food court each month?
Where is the food court located in the mall?
How many restaurants are there in the food court?
Who is the manager of the food court?

Answers

Answer:

A  How many hours do you spend at the food court each month? is a statistical question

Step-by-step explanation:

Because that can have many answers unlike where is the food court in the mall? that question is not statistical because there can only be one answer and so are all the other ones.

Answer:

How many hours do you spend at the food court each month?

Step-by-step explanation:

I just took test got 100% this answer is correct

How many hours do you spend at the food court each month?

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