1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
IrinaK [193]
3 years ago
8

The common ratio of a geometric progression is 1/2 , the fifth term is 1/80 , and the sum of all of its terms is 127/320 . Find

the number of terms in the progression.
Mathematics
2 answers:
sasho [114]3 years ago
7 0

This is what im getting out if it.


1/2 * the fith term with the sum of its terms would equal your % your looking for.


Good luck on your test!

NeTakaya3 years ago
5 0

Answer:

n = 7

number of terms is 7

Step-by-step explanation:

The common ratio is 1/2 of a geometric progression . The fifth term = 1/80

sum of all it terms = 127/320.

The number of term in the progression can be computed as follows:

let us get the first term

nth term = arⁿ⁻¹

where

a = first term

n = number of terms

r  = common ratio

nth term = arⁿ⁻¹

fifth term = 1/80

1/80 = a × 1/2⁵⁻¹

1/80 = a × 1/2⁴

1/80 = a/16

cross multiply

16 = 80a

divide both sides by 80

a = 16/80

a = 1/5

The sum of all terms = 127/320

sum = a(1 - rⁿ)/1 - r

127/320 = 1/5 (1 - 1/2ⁿ)/ 1 - 1/2

127/320 = 1/5(1 - 1/2ⁿ)  / 1/2

127/320 = 2/5(1 - 1/2ⁿ)

127/320 = 2/5 - 2/5 × 1/2ⁿ

collect like terms

127/320 - 2/5 = - 2/5 × 1/2ⁿ

(127 - 128)/320 = - 2/5 × 1/2ⁿ

-1/320 =  - 2/5 × 1/2ⁿ

multiply both sides by -5/2

-1/320 × - 5/2 =  1/2ⁿ

5/640 =  1/2ⁿ

1/128 =  1/2ⁿ

1/2⁷ =  1/2ⁿ

both sides have same base

n = 7

number of terms  = 7

You might be interested in
Five hundred dollars more than 10% of am amount of money $m is $1280. Find m.
In-s [12.5K]
For this one, we need to make an equation to make it look easier
(0.10 × m) + 500 = 1280
We solve for m
Subtract 500 from both sides and we get
0.10 × m = 780
Now, divide both sides by 0.10
And m would be equal to 7800
Let's see if this is correct.
Five hundred dollars more than 10% of m
We found that 10% of m is 780, now we add 500 to make the statement true. It will give us a total of 1280, which is equal of what the question says.
I hope this helps.
YOU'RE WELCOME :D









*brainliest*
6 0
2 years ago
A bookmark has an area of 14 square centimeters and a perimeter of 18 centimeters. What are the dimensions of the bookmark?
Naily [24]

Answer:

2 x 7

Step-by-step explanation:

a * b = 14

2a + 2b = 18

(a * b)/b  = 14/b Dividing both sides by b

a = 14/b

Substitute a in the perimeter equation

2(14/b) + 2b = 18

28/b + 2b = 18

2b - 18 + 28/b = 0

Multiply both sides by b

2b^2 - 18b + 28 = 0

Divide both sides by two

b^2 - 9b + 14 = 0

The Factors of 14 include -2 and -7 which add up to -9

(b - 2) * (b - 7) = 0

This has two answers because b can be either the side that is 2 long or 7 long, so there's no need to go back and solve for a.

2 x 7

4 0
3 years ago
Which set of side lengths form a right triangle?
Reil [10]
I just took the test and the answer was D
50 in, 48 in, 14 in are the side lengths that form a right triangle
4 0
3 years ago
Read 2 more answers
Nick and Monica are paid $41.25 for their work. Nick worked 2.5 hours, and Monica worked 3 hours. They split the money according
vlada-n [284]

Answer:

BRIANLIEST PLZ

N = 18.75

M = 22.5

Step-by-step explanation:

Need the ratio of money paid to each. We know how the ratio of time is divided so we can use this ratio to find the amount paid.

T = t1 + t2 = 2.5 + 3 = 5.5

r1 =2.5/5.5

r2 = 3/5.5

Nick = r1 * 41.25 = 18.75

Monica = r2 * 41.25 = 22.5

7 0
3 years ago
Please Help With this Question ( The Question is EZ im just tired )<br> Will mark brainliest
dlinn [17]

Answer:

put the right point at 80,12 and put the point on the left at 0,0

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • Please help urgent
    14·1 answer
  • Find the sum of the even integers between 21 and 45
    7·2 answers
  • Find the distance between (1,2) and (5,5) .<br> ​<br> ​ helllllllppppp me plzzzz
    14·2 answers
  • carmen wants to tie a piece of ribbon onto balloons for a party. She has a ribbon that is 22 1/2 inches long which she'll cut in
    8·2 answers
  • What is (5^3)6 in index form?
    8·1 answer
  • The figure is made up of a hemisphere and a cylinder.
    5·2 answers
  • What type of world would you want to escape to right now if you could ?
    10·1 answer
  • !!!I’ll mark brainlest and it’s worth 30 points, it’s for a math test and i’m really confused.!!!
    14·2 answers
  • Select all that are equivalent to the expression x^-1/3
    11·1 answer
  • Does anybody knows this if u do please tell me the 3 facts this is due tomorrow!!:[ ​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!