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
USPshnik [31]
3 years ago
14

Fred and Frank play a game. Fred picks an even number X and asks Frank to add all even numbers between 0 and X (inclusive) as fa

st as possible. After some rounds Frank found a quick way to do it. He simply multiplies X/2 by (X/2 + 1). Explain why it always works.
Mathematics
1 answer:
TiliK225 [7]3 years ago
8 0

Answer:

The even numbers between 0 and X represents an arithmetic sequence with a common difference of 2

The rule of arithmetic sequence = a + d(n - 1)

Where a is the first term and n is the number of terms

So, for the even numbers between 0 and X

The first term = a = 0

d = 2

So, we need to find n at the last term which is X

∴ X = 0 + 2 ( n -1 )

∴ n - 1 = X/2

∴ n = X/2 + 1

The sum of the arithmetic sequence = (n/2) × (2a + (n−1)d)

Substitute with a and d and X

So, the sum = (n/2) * (2*0 + (n−1)*2)

                   = (n/2) * ((n−1)*2)

                   = n(n-1)

                   = (X/2 + 1) * (X/2)

                   = X/2 by (X/2 + 1)

So, The quick way to add all even numbers between 0 and X always works.

You might be interested in
∠A and ∠B are supplementary, and ∠A and ∠C are supplementary. Which conclusion is valid? Select one: A. ∠B and ∠C are supplement
zysi [14]

Option D is the correct answer.

Answer:

D. ∠B and ∠C are congruent.

Step-by-step explanation:

Since, ∠A and ∠B are supplementary.

Therefore,

∠A + ∠B = 180°.....(1)

Since, ∠A and ∠C are supplementary.

Therefore,

∠A + ∠C = 180°.....(2)

From equations (1) & (2)

∠A + ∠B = ∠A + ∠C

=> ∠B = ∠C

Hence, ∠B and ∠C are congruent.

4 0
3 years ago
What is the volume of the coffee in a can of the can has a radius of 4 inches and a height of 9inches
posledela

Answer:452.16

Step-by-step explanation: The formula for a cylinder (coffee in a can) is "V=\pir^{2}h"

8 0
2 years ago
Loretta is trying to build the largest taco in the world she uses 2000 pounds of ground beef one tenth as many pounds of cheese
lakkis [162]

Answer:

2000

Step-by-step explanation:


3 0
2 years ago
When making pink paint the teacher use the ratio 3:2 for every 3 cups of white paint she uses in the mixture she needs to use 2
klio [65]
The ratio is 3:2, which equals 1.5
8 0
3 years ago
What is 33/23 rounded to the nearest tenth
Naya [18.7K]

Answer:

1.4

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Help!!!!!!!!!!!!!!!!!
    14·2 answers
  • Explain how you would solve 16/c=8
    5·2 answers
  • Is this a function or no
    11·2 answers
  • Eight more than 3 times a number
    7·2 answers
  • What are the answers to thins? i need all of the blanks filled!
    9·1 answer
  • Calcula el valor de A - B, si se sabe que: A=
    5·1 answer
  • The base edge of the regular triangular pyramid is b=10 cm and altitude of the base hb ≈ 8.66 cm. The slant height of the pyrami
    12·1 answer
  • Help me solve for 20 please ok?
    13·1 answer
  • A factory received a shipment of 11 hammers, and the vendor who sold the items knows there are 2 hammers in the shipment that ar
    15·1 answer
  • Help needed ASAP<br> And thanks!!:)
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!