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
Sergeu [11.5K]
2 years ago
13

Find a formula for the sum of the first n even integers : 2 + 4 + 6 + ... + 2n.

Mathematics
1 answer:
Sedbober [7]2 years ago
7 0

Let S be the sum,

S = 2 + 4 + 6 + ... + 2 (n - 2) + 2 (n - 1) + 2n

Reverse the order of terms:

S = 2n + 2 (n - 1) + 2 (n - 2) + ... + 6 + 4 + 2

Add up terms in the same positions, so that twice the sum is

2S = (2n + 2) + (2n + 2) + (2n + 2) + ... + (2n + 2)

or

2S = n (2n + 2)

Divide both sides by 2 to solve for S :

S = n (n + 1)

You might be interested in
Which of these numbers has the greatest absolute value-3 1 -9 5
Burka [1]
I believe it is the 9, with absolute values the number will always be positive so the absolute value of -9 is 9, which is the greatest out of all the options
3 0
3 years ago
A cliff diver jumps from a ledge 96 feet above the ocean with an initial upward velocity of 16 feet per second. How long will it
Nimfa-mama [501]
In my opinion it would be about 36 seconds

5 0
3 years ago
Read 2 more answers
I would love your guys help!! ASAP!!
sweet [91]

9514 1404 393

Answer:

  1. 3/2
  2. it is the ratio of oil to vinegar in the dressing
  3. y = 3/2x

Step-by-step explanation:

1. The table can be filled in like this:

  • (x, y)
  • (0, 0)
  • (2, 3)
  • (4, 6)
  • (6, 9)

The constant of proportionality is the ratio of y to x:

  k = 3/2

__

2. The meaning of the constant of proportionality is just what it is defined to mean: the ratio of oil to vinegar in the dressing.

__

3. The equation is y=kx, where k is the value in part 1:

  y = (3/2)x

6 0
3 years ago
Ok. Keleiek 2/7=^++^*€€£|€|£|
nikdorinn [45]
What is that??????????????
3 0
3 years ago
Read 2 more answers
I need to know the answer
Mamont248 [21]

she sold a total of 97 shirts, so mulitiply 97 by the profit, which is 27. that gives you the answer of $1649.
8 0
3 years ago
Other questions:
  • For number five I need help plz help
    5·1 answer
  • What is the side length of a cube with a volume of 64 mm3? Cube V = s3   1. Substitute the value into the formula:      64 = s3
    5·2 answers
  • Look at this system of equations. How can the system be changed so that the two equations have equal x-coefficients?
    10·1 answer
  • Plot √0.5 on the number line.
    6·2 answers
  • Plz i need help and FAST!!! Sketch a rectangular prism that has a volume of 36 cubic cm. Label the dimensions of each side on th
    6·1 answer
  • What would x be if the problem is 2x+13
    6·1 answer
  • A premature infant weighing 3lbs is ordered to 1 milligram per gram of a drug. How many milligrams should you administer to the
    6·1 answer
  • PLZ HELP MEEEE NEED ANSWERS ASAP
    10·2 answers
  • PQR is congruent to JKL.<br><br> Which sequence of transformations maps<br> PQR onto JKL?
    7·1 answer
  • EXERCISES
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!