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
qaws [65]
3 years ago
8

Calculate the sum of the multiples of 4 from 0 to 1000

Mathematics
1 answer:
allochka39001 [22]3 years ago
3 0

Answer:

sum is 125,500

sum in summation notation is \sum\limits_{n=0}^n a+nd= (2a+(n-1)d)n/2

Step-by-step explanation:

This problem can be solved using concept of arithmetic progression.

The sum of n term terms in arithmetic progression is given by

sum = (2a+(n-1)d)n/2

where

a is the first term

d is the common difference of arithmetic progression

_____________________________________________________

in the problem

series is multiple of 4 starting from 4 ending at 1000

so series will look like

series: 0,4,8,12,16..................1000

a is first term so

here a is 0

lets find d the common difference

common difference is given by nth term - (n-1)th term

lets take nth term as 8

so (n-1)th term = 4

Thus,

d = 8-4 = 4

d  can also be seen 4 intuitively as series is multiple of four.

_____________________________________________

let calculate value of n

we have last term as 1000

Nth term can be described

Nth term = 0+(n-1)d

1000 =   (n-1)4

=> 1000 = 4n -4

=> 1000 + 4= 4n

=> n = 1004/4 = 251

_____________________________________

now we have

n = 1000

a = 0

d = 4

so we can calculate sum of the series by using formula given above

sum = (2a+(n-1)d)n/2

       = (2*0 + (251-1)4)251/2

       = (250*4)251/2

     = 1000*251/2 = 500*251 = 125,500

Thus, sum is 125,500

sum in summation notation is \sum\limits_{n=0}^n a+nd= (2a+(n-1)d)n/2

You might be interested in
Triangle RST has vertices located at R (2, 3), S (4, 4), and T (5, 0). Part A: Find the length of each side of the triangle. Sho
deff fn [24]

Answer:

(a) Side lengths

RS = \sqrt{5}     ST = \sqrt{17}    RT = \sqrt{18}

(b) Slope

RS = \frac{1}{2}      RT = 1      ST = -4

(c) Scalene triangle

Step-by-step explanation:

Given

R = (2,3)

S = (4,4)

T = (5,0)\\

Solving (a): Length of each side

This is calculated using distance formula

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

So, we have:

RS = \sqrt{(4 - 2)^2 + (4 - 3)^2}

RS = \sqrt{5}

ST = \sqrt{(5 - 4)^2 + (0- 4)^2}

ST = \sqrt{17}

RT = \sqrt{(5 - 2)^2 + (0 - 3)^2}

RT = \sqrt{18}

Solving (b): The slope of each side

This is calculated using:

m = \frac{y_2 - y_1}{x_2 - x_1}

So, we have:

RS = \frac{4- 3}{4- 2}

RS = \frac{1}{2}

RT = \frac{0 - 3}{5- 2}

RT = \frac{ - 3}{- 3}

RT = 1

ST = \frac{0 - 4}{5- 4}

ST = \frac{- 4}{1}

ST = -4

Solving (c): Classify the triangle

In (a), we have:

RS = \sqrt{5}

ST = \sqrt{17}

RT = \sqrt{18}

None of the sides are equal;

The triangle is scalene

5 0
3 years ago
Moises is determining the solution to the system of equations that is show below. Equation representing line A: y = one-third x
FrozenT [24]

Answer:

the answer is B

Step-by-step explanation:

edge2020 just took the test

4 0
3 years ago
Read 2 more answers
How many solutions does this equation have? d − 3 = –3 + d
Tomtit [17]
It has an infinite amount of solutions.

Explanation:
d-3 = -3+d which can be arranged as: d-3=d-3
Since they are equal to each other, no matter what number you input, your solution will be the same which means that there are an infinite amount of solutions. Let’s put this to the test and put in 5 for d. 5-3=5-3 is 2=2. They are equal to each other which means: infinite solution.
4 0
3 years ago
A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance
iren2701 [21]

Answer:

100% of the daily recommended allowance of vitamin C for adults is 80 milligrams.

Step-by-step explanation:

A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults.

100% will have = \frac{200}{250}\times100 = 80 milligrams

Hence, 100% of the daily recommended allowance of vitamin C for adults is 80 milligrams.

8 0
3 years ago
Help needed if you don't mind
laiz [17]

Personification is when an inanimate object is given human-like qualities in writing, so of the options in question 6, the choice with personification in the sentence would be  b. because the World Trade Center does not have footprints, humans do! :)

4 0
3 years ago
Other questions:
  • Plss give step by step solutions !!!!!​
    13·1 answer
  • Please help me<br><br> f(x) =3x^2 + 2x - 1 <br> what is f(5)
    13·2 answers
  • Simplify The Algebraic Expression
    15·1 answer
  • Which graph represents a step function?
    14·2 answers
  • A golf course charges $18 to golf 18 holes and $7 for a cart for a no-member.
    7·1 answer
  • Find the area of the following shape. Show all work
    12·1 answer
  • James bought Nicole a pair of shoes for $54.99 and a bracelet for $21.99. He used a 15% off coupon and then paid 7.5% sales tax.
    10·2 answers
  • 1. Write a recursive formula for the following sequence: <br><br> 45, 41, 37, 33
    14·2 answers
  • What is value of x need help ASAP if so
    11·2 answers
  • The temperature dropped 14.4 over a period
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!