Let's see what to do buddy...
_________________________________
Step (1)
Suppose we want to find the sum of numbers from 1 to n.
To do this, we use the following method.
By writing the sum of numbers from 1 to n
, Then we write the sum of numbers n to 1 below it, see :
[tex]s = 1 + 2 + 3 + ... + n[/tex]
[tex]s = n + (n - 1) + (n - 2) + ... + 1 \\ [/tex]
Now we add the sentences of the above two phrases, peer to peer like this :
[tex]1 + n = n + 1 \\ [/tex]
[tex]2 + n - 1 = n + 1[/tex]
[tex]3 + n - 2 = n + 1[/tex]
And the others.....
So we have :
[tex]2s = ( n + 1) + (n + 1) + ... + (n + 1) \\ [/tex]
We had n numbers to sum so we have :
[tex]2s = n \times (n + 1)[/tex]
Divided the sides of the equation by 2
[tex]s = \frac{n \times (n + 1)}{2} \\ [/tex]
Remember this step I will use it again.
_________________________________
Step (2)
What does the linear sequence mean ?
The linear sequence is the sequence which any terms created by the sum of previous term with constant.
I name that constant value d.
According to above :
[tex]t(2) = t(1) + d[/tex]
And
[tex]t(3) = t(2) + d [/tex]
[tex]t(3) = t(1) + d + d[/tex]
[tex]t(3) = t(1) + 2d[/tex]
I have a question ;
[tex]3 - 1 = 2[/tex]
Is it correct ?
If it is correct we have :
[tex]t(3) = t(1) + (3 - 1)d[/tex]
WOW we found a thing ;
Put n instead of 3 :
[tex]t(n) = t(1) + (n - 1)d[/tex]
_________________________________
Step (3)
Stop right here.
Let's go to find the sum of the n first terms of the linear sequence.
Do you remember what did we do in step(1) ? Of course you do.
Let's do it again.
[tex]s = t(1) + t(2) + t(3) + ... + t(n) \\ [/tex]
[tex]s = t(n) + t(n - 1) + t(n - 2) + ... + t(2) + t(1) \\ [/tex]
According to the thing what we found in step(2) we have :
[tex]s = t(1) + ( \: t(1) + d \: ) + ( \: t(1) + 2d \: ) + ... + ( \: t(1) + (n - 1)d \: ) \\ [/tex]
[tex]s = ( \: t(1) + (n - 1)d \: ) + ( \: t(1) + (n - 2)d \: ) + ... + t(1) \\ [/tex]
Sum the two above equation's terms like this:
[tex]t(1) + t(1) + (n - 1)d = 2t(1) + (n - 1)d \\ [/tex]
And
[tex]t(1) + d +t(1) + (n - 2)d = 2t(1) + d(n - 2 + 1) = 2t(1) + (n - 1)d \\ [/tex]
And the others like this.
We had n terms so we sumed n terms.
So we have :
[tex]2s = n \times ( \: 2t(1) + (n - 1)d \: )[/tex]
Divided the sides of the equation by 2
[tex]s(n) = \frac{n}{2} \times ( \: 2t(1) + (n - 1)d \: ) \\ [/tex]
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
I WILL GIVE BRAINLIEST!!!
Answer:
B
Step-by-step explanation:
Basically, both have a helmet rate of $5/hr. So,
300 +5x and 25x+5x = 30x
The questions specifically wants the purchasing to be lower.
I need helllpppppppp please
Answer:
A. $482.20
Step-by-step explanation:
All amounts shown are deductions, so add all amounts.
$180.00 + $25.00 + $200.20 + $77.00 = $482.20
Answer: $482.20
State the domain plssssa
Answer:
I think it's {3, 6, 12, 18}
Step-by-step explanation:
Domain: all x-values that are to be used (independent values).
The formula P= 2/+ 2w means that the perimeter of a rectangle is equal to
twice the sum of its length and its width.
Solve P = 21+ 2 w for /
Answer:
D. [tex] l = \frac{P - 2w}{2} [/tex]
Step-by-step explanation:
Given:
[tex] P = 2l + 2w [/tex]
Required:
Solve for l
Solution:
To solve for l, we would make l the subject of the given formula.
[tex] P = 2l + 2w [/tex]
[tex] P = 2(l + w) [/tex]
Divide both sides by 2
[tex] \frac{P}{2} = \frac{2(l + w)}{2} [/tex]
[tex] \frac{P}{2} = l + w [/tex]
Subtract w from both sides
[tex] \frac{P}{2} - w = l + w - w [/tex]
[tex] \frac{P}{2} - w = l [/tex]
[tex] \frac{P}{2} - \frac{w}{1} = l [/tex]
[tex] \frac{P - 2w}{2} = l [/tex]
Rewrite
[tex] l = \frac{P - 2w}{2} [/tex]
In this picture, the measure of angle ois 1 radian.
A. True
B. False
Answer: the answer is true I think
Step-by-step explanation:
Suppose you have a total of $2.25 in dimes and
nickels. You have twice as many dimes, as nickels.
Which system of equations could be used to
determine how many of each coin you have?
Answer:
n = number of nickels
2n = number of dimes
n($0.05) + 2n($0.10) = $2.25
0.05n + 0.2n = 2.25
0.25n = 2.25
n = 2.25/0.25 = 9
2n = 2(9) = 18
You has 9 nickels and 18 dimes
Step-by-step explanation:
Find the LCM of 6 and 5
Answer:
30
Step-by-step explanation:
Answer:
there right
Step-by-step explanation:
Simplify. .
-(2x – Зу) + 5х + 2 – 3х + Зу + 2
А. 4
В. 4х + 4
С. 6y + 4
D. 4х + бу + 4
Please select the best answer from the choices provided
A
B
ОООО
С
D
Answer:
6y+4
Step-by-step explanation:
-(2x-3y) +5x +2 -3x +3y +2
(-2x -3x +5x) (3y +3y) (2 +2)
0 +6y +4
6y +4
81 - 100a2
What is the answer
Answer:10a
Step-by-step explanation:
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
9
and
b
=
10
a
.
(
9
+
10
a
)
(
9
−
10
a
)
6. XY = 5x, YZ = X, and XY=25
Answer:
its cartesian Product of XY * YZ is {{5x,X}}
its cartesian Product of YZ * XY is {{x,5X}}
need it in a diffrent form? just ask
I hope this helps
if you could, feel free to mark me Brainliest it would be much appreciated :D
7th grade math help me pleasee
Answer: 15 + (-35) = -20
Step-by-step explanation: This is the addition equation for your question.
Answer:
15 plus -15 plus -20
Step-by-step explanation:
15 plus -15 equals zero, when we add a the a negative and a positive of the same number it's a zero. And I add -20 to go down instead of subtracting.
~~Hope this helps~~~ :)
A purple hot-air balloon is 90 feet off the ground and rising at a rate of 7 feet per second. A yellow hot-air balloon is 120 feet off the ground and rising at a rate of 4 feet per second. Which equation could represent this situation and determine after how many seconds, s, the purple hot-air balloon will be the same height as the yellow hot-air balloon?
1 point
90 + 7s = 120 + 4s
7s + 120 = 4s + 90
90s + 7 = 120s + 4
11s = 210
90+7s = 120 + 4s
11s = 210
Which three lengths could be used to form a right triangle ?
Which of the following shows an example of the identity property of 0? Select one: a. 1/2+1/2=1 b. 22/7+(-22/7)=0 c. 0+(-7 5/6)=-7 5/6 d. -3 1/4+6 1/2=3 1/4
The example of the identity property of 0 will be 0 + (–7 5/6) = –7 5/6. Then the correct option is C.
What is identity property of addition?According to the identity property of addition, any value is that summation of 0 and any other value.
a + 0 = a
The example of the identity property of 0 will be
0 + (–7 5/6) = –7 5/6
Then the correct option is C.
More about the identity property of addition link is given below.
https://brainly.com/question/1709448
#SPJ2
Need help please badly
Answer:
CED is a right angle, CEB=AEB
hopw that helps
Answer:
1st, 2nd, 5th
Step-by-step explanation:
Which two operations are needed to write the expression that represents "eight more than the product of a number and
two"?
A. multiplication and subtraction
B. division and subtraction
C. multiplication and addition
D. division and addition
PLEASE HELP
HELP PLEASE I am in elementary school don’t make fun of me but this is my Q: 274/385 + 583/648
Answer:
402007/249480
Step-by-step explanation:
or decimal form: 1.61137966
Solve this equation
100x + 300 = 200
Answer:
-1
Step-by-step explanation:
100x=200-300
100x=-100
100x/100=-100/100
x=-1
After solving this equation we get, 100x + 300 = 200 x = -1.
To solve this equation
100x + 300 = 200,
Subtract 300 on both side,
100x + 300 - 300 = 200 - 300
100x = -100
Divide 100 on both side,
x = -1
Therefore, After solving this equation 100x + 300 = 200 we get x = -1.
Learn more about How to solve equation here;
https://brainly.com/question/13594275
#SPJ6
what is 49.672 to the nearest hundredth
Answer:
49.680
Step-by-step explanation:
the tenth is not small
A bag contains 3 red marbles, 8 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that all three marbles drawn will be green?
Answer:
A bag contains 8 red marbles, 3 blue marbles and 7 green marbles.
Total = 18 marbles.
Probability of drawing three red marbles = probability of drawing one red without replacement + probab of drawing another without reeplacement + probab of drawing a third without replacement.
Probability of drawing three red marbles = 8/18 + 7/17 + 6/16 = 0.4444 + 0.4118 + 0.3750 = 1.2312.
Answer:
0.043
Step-by-step explanation:
Which of these is an opinion
(helppp)
Answer:
A
Step-by-step explanation:
because all the other ones are facts
A square field has 3,844 sq. meters of land. What is the width of the field?
Answer:
The side length is 62 meters
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
3844 m^2 = s^2
Take the square root of each side
sqrt( 3844 m^2) = sqrt(s^2)
62 m= s
The side length is 62 meters
What is the difference between the longest jump and the shortest jump in the running long jump event?
Josie deposited $450 in a bank account
Answer:
What is the question?
Step-by-step explanation:
Deposit means add so he added $450 to his bank account
What does “each point of a line maps to itself” mean? I don’t understand it what it means for it to map to itself.
Answer:
Step-by-step explanation:
For example if you have a function f(x) = x - 1, then x = 1 is a zero of this function because using it as x gives 1 - 1 = 0. The Riemann Zeta function has some zeros that are easy to find which are of little interest but there are some other ones that are harder to find which is why the are called non-trivial.
hcf of 72, 120, 192 with explanations
1.
Only one-fourth of Earth’s surface is land, but land constitutes over 99% of the Earth’s actual mass. Which sphere of the Earth does this statement describe?
biosphere
lithosphere
atmosphere
hydrosphere
Answer:
Lithosphere.
Step-by-step explanation:
Lithosphere is known for being the Earth's sphere ehre all rocks and types of land are included. Therefore, if land constitutes over 99% of the Earth's actual mass, then the statement is refering to the Lithosphere.
In this question, you are asked to specify the sphere of the earth described in the sentence
The sphere of the earth described in the sentence is lithosphere.
Lithosphere is the sphere of the earth which consists of land.Biosphere is the portion of the earth which constitutes lives. Living organisms live in this part of the earth.Atmosphere consist of the gaseous part of the earth. Hydrosphere is the portion of the earth that consist of water either fresh or salt waterRead more:
https://brainly.com/question/10893109
Evaluate the function: f(n) = n + 4
Find: f(-9)
Evaluate the function
Fill in the missing num W + 2 7 9 2
Answer:
What are you asking? What does it equal? W+2792=??
Answer:
there is no number that could fit, it actually could be anything, I think that there is a part of the problem not there that is a expression to solve that you need a equation
Step-by-step explanation:
Change each percent to a decimal or a mixed decimal
43%
2 1/2%
13.6%
521%
Step-by-step explanation:
43%=43/100
21/2%=1050
13.6%=136/100
521%=521/100
