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
Four students took a national standardized test for which the mean was 500 and the standard deviation was 100. If a student’s z-
murzikaleks [220]

z = (x - 500) / 100

1.75 = (x - 500) / 100

175 = x - 500

675 = x

3 0
3 years ago
Read 2 more answers
How would I solve for V?<br><img src="https://tex.z-dn.net/?f=ke%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E%7B2%7D%20" id="TexForm
Shkiper50 [21]

(i just changed my answer)

sqrt is the square root of

v=sqrt(2(ke)/m)

4 0
3 years ago
Please help!!
vodomira [7]

Answer:

The population will be 240,116

Step-by-step explanation:

Exponential growth can be represented by the expression:

P(t) = P_i\,(1+r)^t

where:

P(t) is the population at time (t)

P_i is the initial value of the population

"r" is the annual rate of growth (written in decimal form)

and "t" is the time in years.

Therefore in this situation, P(16) is what we want to find [the population after 16 years]

the initial population P_i is 110,000

the rate of growth is 0.05 [decimal form of 5%]

and t is 16 years.

Replacing all these in the given functional form gives:

P(t) = P_i\,(1+r)^t\\P(16)=110000\,(1+0.05)^16\\P(16)=240116

4 0
3 years ago
Answer this geometry question
Basile [38]
The measure of the angle formed by 2 chords  that intersect inside the circle is 1/2 the sum of the chords' intercepted arcs. 
m∠RST = (143+33)/2 = 176/2 = 88°
6 0
3 years ago
Find the slope that passes thru (3,5) and (5,8)
Anni [7]
Would it be 3/2 since it’s rise over run with 3 on the x line to 5 and 5 on the y line to 8
3 0
3 years ago
Other questions:
  • What is310763136 in word form
    7·1 answer
  • 331/3% of what number is 57
    12·1 answer
  • Find the constant of variation (k) where y varies directly with x. y = 2, when<br> X = 6.
    6·1 answer
  • please answer this correctly....1.A bag contains 5 red marbles, 6 green marbles, and 3 blue marbles. If Cymra draws a marble, ke
    11·1 answer
  • Researchers fed mice a specific amount of Toxaphene, a poisonous pesticide, and studied their nervous systems to find out why To
    13·1 answer
  • Which expression represents the approximate length of bc?
    10·2 answers
  • In the figure, PA and PB are tangent to circle O and PD bisects ∠BPA . The figure is not drawn to scale. For m
    9·1 answer
  • What makes values of a and b make each inequality true? -ab&gt;0, ab&lt;0, a^2b&gt;0, a/b&gt;0
    15·1 answer
  • Which scenario best matches the inequality x&gt;3?
    14·2 answers
  • Fractions. Subtraction with Renaming<br><br> 8 wholes and 1/6 minus 3 wholes and 5/6
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!