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
Andrew [12]
3 years ago
6

There are ‘n’ arithmetic means between 33 and – 3. If second last mean: second mean = 1: 5, find the value of n.

Mathematics
1 answer:
Delicious77 [7]3 years ago
7 0

We know that:

There are n arithmetic means between the numbers 33 and -3

second last mean: second mean = 1:5

Using this, we can find that the value of n is 9.

Now let's see how we need to use the information.

"There are n arithmetic means between the numbers 33 and -3"

This means that we will have a sequence like:

33, a₁, a₂, ..., aₙ, -3

And by the given ratio, we know that:

aₙ₋₂:a₂  = 1:5

Also, because this is an arithmetic sequence we have:

a₁ = 33 + d

a₂ = 33 + d + d

aₙ ₋ ₂ = 33 + (n - 2)*d = -3 - 2*d

Because of the ratio, we will have that:

aₙ₋₂/a₂ = 1/5

We can replace what the left side by:

(-3 - 2*d)/(33 + 2*d) = 1/5

now we can solve this for d.

-3 - 2*d = (33 + 2*d)*(1/5)

5*(-3 - 2*d ) = (33 + 2*d)

-15 - 10d = 33 + 2d

-15 - 33 = 2d + 10d

-48 = 12d

-48/12 = -4 = d

So now we know that the value of d is -4.

Now we can use the equation

aₙ ₋ ₂ = 33 + (n - 2)*d = -3 - 2*d

to find the value of n:

33 + (n - 2)*d = -3 - 2*d

33 + (n - 2)*-4 = -3 - 2*-4

33 - 4n + 8 =  -3 + 8

41 - 4n = 5

-4n = 5 - 41 = -36

n = 36/4 = 9

The value of n is 9.

If you want to learn more, you can read:

brainly.com/question/11559160

You might be interested in
Determine the domain and range of the given function.
frez [133]

Answer: domain is all real numbers and range is all real numbers greater than or equal to -2

Step-by-step explanation:

7 0
3 years ago
If m∠NLO = 41° and m∠NLM = 88°, what is m∠OLM?
puteri [66]

Answer:

47°

Step-by-step explanation:

Given that m<NLO = 41°, and m<NLM = 88°, according to angle addition postulate, m<OLM + m<NLO = m<NLM

Therefore, subtracting m<NLO from both sides will give us:

m<OLM = m<NLM - m<NLO

m<OLM = 88° - 41°

m<OLM = 47°

5 0
3 years ago
The sum of 3x and 14 equals the difference of 20 and 2x
KonstantinChe [14]

Answer. 17<18

The sum of 3x + 14 equals 17x.

The difference between 20 - 2x equals 18x.

Therefore the equation is not equal to each other.

6 0
3 years ago
A rectangular patio has the length of 12 1/2 feet in an area of 103 and 1/8 ft.what is the width of the patio
Scrat [10]
A=LW
103 1/8=12 1/2W
103 1/8 divided by 12 1/2
8 1/4
7 0
3 years ago
Rewrite, using the distributive<br> property.<br> 5(2x – 3y) = [?]x-[ ]y
fenix001 [56]
Answer: 10x - 15y because 5(2x) = 10x and 5(-3y) = -15y
8 0
2 years ago
Other questions:
  • Which number is a solution of the inequality
    12·1 answer
  • Need help please and thanks​
    12·1 answer
  • What is 12:34 and 19:56
    15·2 answers
  • Jord Problems
    10·1 answer
  • A test of a printed circuit board uses a random test pattern with an array of 8 bits and each is equally likely to be 0 or 1. Wr
    12·1 answer
  • What value of x will make △ONM similar to △SRQ by the SAS similarity theorem?
    15·2 answers
  • Which point could be removed in order to make the relation a function?
    14·1 answer
  • at a certain time of day, a tree that is X meters tall casts a shadow that is x-34 meters long. if the distance from the top of
    9·1 answer
  • The weight of an object on Mars is about 2/5 its weight on Earth. How much would an 80 1/2 pound dog weight on Mars?
    6·1 answer
  • Please answer and explain.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!