How can you find the sum of the first 5 consecutive positive integers? You can easily add the numbers mentally—the sum is 15. But what if you want to find the sum of the first ​n ​consecutive whole numbers? Keep this question in mind and make some conjectures about a formula.

Answers

Answer 1

Given:

First five consecutive positive integers.

To find:

The sum of the first 5 consecutive positive integers.

Sum of the first ​n ​consecutive whole numbers.

Solution:

First five consecutive positive integers are 1, 2, 3, 4 and 5.

Sum of these numbers is

[tex]1+2+3+4+5=15[/tex]

Therefore, the sum of the first 5 consecutive positive integers is 15.

First ​n ​consecutive whole numbers are 0, 1, 2, 3,..., (n-1). These numbers are in AP.

Here, first term is 0 and common difference is 1.

Sum of n terms of an AP is

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

where, a is first term and d is common difference.

Substitute a=0 and d=1 in the above formula.

[tex]S_n=\dfrac{n}{2}[2(0)+(n-1)(1)][/tex]

[tex]S_n=\dfrac{n}{2}[n-1][/tex]

Sum of first 5 consecutive positive integers is equal to the sum of first 6 consecutive whole number because in whole numbers 0 is extra number.

For n=6,

[tex]S_6=\dfrac{6}{2}[6-1][/tex]

[tex]S_6=3(5)[/tex]

[tex]S_6=15[/tex]

The sum of the first 5 consecutive positive integers is 15.

So, the sum of (n-1) consecutive positive integers is

[tex]S_n=\dfrac{n}{2}[n-1][/tex]


Related Questions

Please send an answer quick I really need it the picture is above.

Answers

Answer:

-132

Step-by-step explanation:

When you plug in -8 to every x you get -2(8)^2+2(8)-20 which gives you -132.

7) Write an equation in point-slope form of the line
through point J(-2,10) with slope - 2

Answers

Answer:

y=-2x+6

Step-by-step explanation:

y=mx+b

10=(-2)(-2)+b

10=4+b

10-4=b

6=b

Help please!!!

Question 6
5 pts
Factor the variable expression:
36X + 8X
0419x-4)
4X (9+2)
9(4X+2x)
8(X+X)

Answers

Answer:

4x (9+2)

Step-by-step explanation:

36x+8x

36 and 8 can be divided by 4 and they both have an x

[tex]36x + 8x = 4x(9 + 2)[/tex]

[tex]44x = 36x + 8 x[/tex]

[tex]44x = 44x[/tex]

The Answer is

[tex] \green {\boxed{4x(9+2)}}[/tex]

#IfWrongPleaseReport

#StudyTogetherWithMe

#ILoveMath

Can someone answer this?

Answers

Answer:

y = 1500 + 800x

Step-by-step explanation:

This is the answer because Elisa charges 1500 dollars no matter what. That value is not dependant on anything. Every hour she is with the client is 800 dollars. That is why it is represented as 800x. X being the amount of hours. You add the two together to find how much Elisa's services cost.

Hector is dividing students into groups for a nature hike. He wants to divide the boys and girls so that each group has the same number of both boys and girls. There are 21 boys and 56 girls signed up for the hike. Into how many groups can the students be divided? How many boys and how many girls will be in each group?

Answers

Answer: The students can be divided into 7 groups.

Each group will have 3 boys and 8 girls.

Step-by-step explanation:

There are 21 boys and 56 girls.

To divide them so that each group has the same number of both boys and girls.

We find GCD(21,56).

21 = 3 x 7

56 = 2 x 2 x 2 x 7

GCD (21,56) = 7

So, the students can be divided into 7 groups.

Number of girls in each group = [tex]\dfrac{56}{7}=8[/tex]

Number of boys in each group = [tex]\dfrac{21}{7}=3[/tex]

So, each group will have 3 boys and 8 girls.

Make s the subject of the formula

T^2=2p+as

Answers

Step-by-step explanation:

Original formula: T^2 = 2p + as

T^2 - 2p = as

s = (T^2 - 2p) / a

what is (3,0) reflected on the y-axis

Answers

Reflecting across the y axis, the x value becomes opposite and the y value remains the same.

(3,0) becomes (-3,0)

Answer:

(-3, 0)

Step-by-step explanation:

There is the same amount of units from either side of the y-axis to the points.

what is the point if (2,0) gets rotated 180° clockwise

Answers

Answer:

The point is (0,-2)

Y=9x+2x please help, i don't know how to
do this stuff

Answers

Answer: I hope you understand, just mutiply whatever x is by 11 to get Y

Step-by-step explanation:

x = unknown number

9x+2x= 11x

Y=11x

Is (1,1) a solution to this system of inequalities

Answers

Answer: No

Explanation: It doesn’t work

13 PLS TELL ME THE EQUATION AND HOW TO SOLVE IT WITH THE ANSWER

Answers

Answer:

b

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This triangle should be 180 degrees.

So you should add 80 and 45 and subtract it from 180 to get x.

Find the slope from the table

Answers

Answer:-4/1

Step-by-step explanation:

Point S is the _ of UT?

Answers

Answer:

V

Step-by-step explanation:

SV is correct because it is the same

length of UT. You can check by using

your fingers to check the length of

UT then turn the picture around to

see if it is equal.

Hope this helps! <3

Answer:

S is the midpoint of UT

Step-by-step explanation:

US = ST   -----> from the picture

So, S is the mid point

In a certain fraction, the denominator is 4 larger than the numerator. If 2 is added to both the numerator and the denominator,the result is 3\5. Find the original fraction. PLS ANSWER ​

Answers

Step-by-step explanation:

Here you go, I tried my best

cheers

The original fraction is [tex]\frac{4}{8}[/tex]

Let the numerator = a

Let the denominator = b

Denominator is 4 larger than the numerator: b = a + 4

2 is added to both the numerator and the denominator: (a + 4 +2) and a + 2

The algebraic equation from the given statement is formed as follows;

[tex]\frac{a+ 2}{a+4+2 } = \frac{3}{5} \\\\\frac{a+ 2}{a + 6} =\frac{3}{5} \\\\5(a + 2) = 3(a + 6)\\\\5a + 10 = 3a + 18\\\\5a - 3a = 18 -10\\\\2a = 8\\\\a =4[/tex]

The original fraction is calculated as follows;

[tex]\frac{a }{a +4} = \frac{4}{4+ 4} = \frac{4}{8}[/tex]

Thus, the original fraction is [tex]\frac{4}{8}[/tex]

Learn more here: https://brainly.com/question/16889590

Question 3 of 10
What is the slope of the line given by the equation below?
y + 2 = -3(x-5)
A. -5
B. 3
C. -3
D. 2

Answers

The answer is -3 !

Explanation:

Please give brainliest

Leo the Rabbit

Leo the Rabbit is climbing up a flight of 10 steps. Leo can only hop up 1 or 2 steps each time he hops. He never hops down, only up. How many different ways can Leo hop up the flight of 10 steps? Provide evidence to justify your thinking.

Can someone provide an answer and explain. Thanks

Answers

Answer:

2?

Step-by-step explanation: because he can hop them one step at a time or two steps at a time

What is the slope of this graph?


4

−14

−4

14

Answers

The answer is -4 times


Answer:

-4

Step-by-step explanation:

i took the  quiz on  k12 :)

Point B is located at (0, 2) and is translated to point B' with coordinates (1, -1), which translation did point B undergo? One unit right and three units down One unit right and one unit down Two units right and two units down Three units left and one unit up

Answers

Answer:

One unit right and three units down

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, dilation, rotation or translation.

If a point X(x,y) is translated a units right and b units up, its new location is at X'(x + a, y + b) while if a point is translated a units left and b units down, its location is X'(x - a, y - b).

Since point B is located at (0, 2) and translates to B' with coordinates (1, -1), the translation is given as (x + 1, y - 3) that is 1 unit right and 3 unit down.

In the book,the distance between two planets is given as 4.07×10^¹² kilometres. The speed of light is 1.1×10^⁹ kilometres per hour. Calculate the time taken for light to travel from one of these planets to the other. Give your answer in days and hours.

Answers

Answer:

3700hours

154days

Step-by-step explanation:

Speed can be defined as the distance cover per time, it can be expressed as

Speed= distance/ time........eqn(1)

Given:

distance between two planets= 4.07×10^¹²

speed of light = 1.1×10^⁹ kilometres per hour

Time= ??

Then substitute the values into equation (1) we have

Speed= distance/ time

1.1×10^⁹ kilometres per hour= 4.07×10^¹²kilometre/ time

Cross multiply, we have

Time= (4.07×10^¹²kilometre) /(1.1×10^⁹ kilometres per hour)

Time= 3700hours.

To convert to day, we know that

60 minute= 1hour

24hour=1day

Time= (3700hour×1day)/24hour

Time= 154days approximately.

Hence, the time taken for light to travel from one of these planets to the other is 154days or 3700hours

For each value of x, determine whether it is a solution to x - 42 = 7.​

Answers

Answer:

67- No  46-No   49-Yes   47-No

Step-by-step explanation:

Hope this helps!

Answer:

67...No

46...No

49...Yes

47...No

Step-by-step explanation:

x - 42 = 7

Add 42 to both sides

x = 49

M to the power of 5 n to the power of 3 divided by m to the power of 2 n to the power of -4

please solve fast I will mark the first answer as brainliest and give with step by step explanation ​

Answers

When you divide exponents, you subtract the powers.
m^5/m^2 = m^3
n^3/n^-4 = n^7

Answer is (m^3)(n^7)

If a = 8 in and b = 15 in what is the length of leg c in a right triangle using the
pythagorean theorem?

Answers

So a²+b²=c²
8²+15²=c²
64+225=c²
289=c²
±17=c
So c=17 or c=-17

See attachment for math work and answer.

What is a good problem to use for an inequality equation? using ax + b > c. Including the solution.

Answers

Answer:

A "solution'' of an inequality is a number which when substituted for the variable makes the inequality a true statement. When we substitute 8 for x, the inequality becomes 8-2 > 5. Thus, x=8 is a solution of the inequality.Step-by-step explanation:

Answer:

the person above me is correct

Shark  boi U~U

PLEASE HELP, GIVING BRAINLIEST!!!

These triangles are congruent by _____.

A. SAS
B. AAS
C. SSS
D. Not enough information
E. None of these

Answers

Answer:

I think it might be C...

2. A train starts its journey with 240 passengers.
144 of the passengers are adults and the rest are children.
(a) Write the ratio Adults: Children in its lowest terms.
[2]
(b) At the first stop, 37 % of the adults and of the children get off the train.
20 adults and x children get onto the train.
The total number of passengers on the train is now 200.
(i)
How
many children got off the train?
(ii)
How
many adults got off the train?
[1]
(iii) How many adults passengers are on the train as it sets off again? [1]
(iv) What is the value of x?
[1]

Answers

Answer:

i=52

ii=32

iii=54

iv=92

Step-by-step explanation:

Comment if you need explanation

Answer:

A. 3:2

B. 31 children

(i). 35 children

(ii) 53 adults

(iii) 111 adults 89 children

(iv) The value of x is 35.

Step-by-step explanation:

Which method represents a correct way to solve the equation?

-x+(-3+x)2 = 6

Multiply -3 by 2.

Multiply x by 2.

Combine like terms.

Subtract 6 from both sides.

Use the quadratic formula to solve for x.

OA.

Square -3.

Square x.

Subtract -7x from both sides.

OB. Subtract 9 from both sides.

Take the square root of both sides.

Square -3.

Square x.

Combine like terms

OC. Subtract 6 from both sides.

Use the quadratic formula to solve for x.

OD

Square the quantity (-3 + x).

Combine like terms.

Subtract 6 from both sides.

Use the quadratic formula to solve for x.

Answers

Answer:

Multiply -3 by 2.

Multiply x by 2.

Combine like terms.

Subtract 6 from both sides.

Use the quadratic formula to solve for x.

Step-by-step explanation:

Given:

-x (-3 + x )2 = 6

-x (-3 + x )2 = 6

-x (-6 + 2x) = 6

-6x + 2x^2 = 6

2x^2 - 6x - 6 = 6 - 6

2x^2 - 6x - 6 = 0

Multiply -3 by 2.

Multiply x by 2.

Combine like terms.

Subtract 6 from both sides.

Use the quadratic formula to solve for x.

Write four different equations that have –3 as the solution

Answers

1 + -4

2 + -5

3 + -6

4 + -7

Answer:

5 + -8

6 + -9

7 + -10

8 + -11

Step-by-step explanation:

PLEASE HELP FAST. WILL MARK AS BRAINLIEST IF GIVEN GOOD ANSWER ​

Answers

Answer:y=9

Step-by-step explanation:

Whats the answer? I will give brainliest if correct♡︎ꨄシ

Answers

Answer:

b isnt a fuction

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Help me please need help

Answers

Answer:

w = 10

Step-by-step explanation:

I did the math and and I got 10

Hope it helps!! :D

Answer:

w = 10?

Step-by-step explanation:

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