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
Inga [223]
3 years ago
9

The first three terms of an arithmetic progression are m,12 and n . Find the value of m+n​

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
3 0
<h3>Answer:  24</h3>

===========================================

Explanation:

There are a few approaches. Here's one way to solve.

Let d be the common difference between the terms.

We add d to each term of this arithmetic sequence to get the next term.

  • First term = m
  • Second term = 12 = m+d
  • Third term = n = (m+d)+d = m+2d

Focusing on the second equation, we can solve for d like so

m+d = 12

d = 12-m

This is then plugged into the third equation

n = m+2d

n = m+2(12-m)

n = m+24-2m

n = 24-m

Therefore,

m+n = m+(24-m) = 24

It turns out that it doesn't matter what m and n are because m+n is always equal to 24 in this case.

-----------------

A more concrete example:

Let's say m = 2. We won't set up n just yet but we'll be able to compute it fairly soon.

Since m = 2, this means d = 12-m = 12-2 = 10. This is the gap between adjacent or neighboring terms.

If d = 10, then the third term must be n = 12+d = 12+10 = 22

We can then see that m+n = 2+22 = 24

-----------------

I'll do another example:

m = 5

d = 12-m = 12-5 = 7

n = 12+d = 7 = 19

m+n = 5+19 = 24

Whenever in doubt, or if you get stuck, it helps to come up with actual numeric values to hopefully clear things up.

-----------------

An alternative way to get the answer:

Let's try to determine what m+n is actually saying. We have 12 right in the middle of the first term (m) and third term (n). Because the gap between the numbers is the same (that being d), we know that 12 is the midpoint of m and n. It might help to draw out a number line to see what's going on.

The midpoint of m and n is (m+n)/2

Set this equal to 12 and isolate the "m+n"

(firstTerm+thirdTerm)/2 = second term

(m+n)/2 = 12

m+n = 2*12

m+n = 24

So in general, if the first three terms of the arithmetic sequence are m, k, n, then m+n = 2k.

You might be interested in
What is1/12+7/9. I need help.
Katarina [22]
You have to make them have their least common denominator to add or subtract, in this case 36.
Multiply 1/12 by 3, to get the denominator 36: 3/36.
Multiply 7/9 by 4, to get the denominator 36: 28/36.
Now add the numerators: 3+28=31, 31/36 is as simplified as possible so your answer is 31/36 :) I hope this helps :)
7 0
3 years ago
The converse of the statement “If a quadrilateral has four right angles, then it is a rectangle” is "______."
Nataly [62]
A quadrilateral because you just reverse the question.
6 0
3 years ago
Notah lives in Minnesota. He records the lowest temperature each day for one week. What is the mean of the temperatures? -7.3°F,
natita [175]

Answer:

-2.1

Step-by-step explanation:

-7.3 - 11.2 - 1.7 + 0 + 0 +2.2 + 3.3

--------------------------------------------------

                            7

= -2.1

4 0
2 years ago
Read 2 more answers
Adam has 16.45 kg of flour, he uses 6.4 kg to make hot cross buns. The remaining flour is exactly enough to make 15 batches of s
Doss [256]

Answer:

Each batch of scones needed 0.67 kg of flour

Step-by-step explanation:

16.45 - 6.4 = 10.05kg (remaining)

15 batches = 10.05kg

1 batch = 0.67kg

6 0
3 years ago
Mrs. Van and her family went bowling. The total cost of the shoes was $12 and the cost to bowl was $5 per game. Write an equatio
serious [3.7K]

y=5x+12

hope i could help!

5 0
2 years ago
Other questions:
  • 4/5 os the fourth multiple of what unit fraction?
    7·2 answers
  • Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly a
    9·1 answer
  • The length of a rectangle is 4m more than the width.The area of the rectangle is 45 m^2.find the length
    9·1 answer
  • 10) PLS HELP ASAP!!!<br><br> 10 + POINTS AND BRAINLIEST
    6·2 answers
  • Graph the equation x+4y=12 by plotting points.
    15·1 answer
  • What is the answer of the rectangular prism?<br> 3 1/3 times 1 2/5
    13·1 answer
  • Expand the following:<br> a) 2(x+3)<br> b) 512x-4)<br> C) 4(2x + 1)<br> d) 6 x - 4y
    10·1 answer
  • Ralph Chase plans to sell a piece of property for ​$150000. He wants the money to be paid off in two ways a - ​short-term note a
    5·1 answer
  • Please help, this is geometry
    9·1 answer
  • Points A, B, C, and D lie on circle M. Line segment BD is a diameter. The measure of arc CD equals the measure of arc DA.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!