prove that Sn=n(n+1) for the sequence an=2n,where n is any positive integers​

Answers

Answer 1

Answer:

Proved

Step-by-step explanation:

Given

[tex]a_n = 2n[/tex]

Required

Prove that [tex]S_n = n(n+1)[/tex]

The given sequence is an arithmetic sequence.

The Sn of this sequence is:

[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]

Calculate a1

[tex]a_n =2n[/tex]

[tex]a_1 =2*1[/tex]

[tex]a_1 =2[/tex]

So, we have:

[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]

[tex]S_n = \frac{n}{2}(2 + 2n)[/tex]

Factor out 2

[tex]S_n = \frac{n*2}{2}(1 + n)[/tex]

[tex]S_n = n(1 + n)[/tex]

[tex]S_n = n(n + 1)[/tex] --- Proved


Related Questions

Can someone explain to me how to do this problem?
x • 1 + x/1 =

Answers

x • 1 + x/1
x + x/1
2x/1
=2x

Fine the exponent ??

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Answer:

the exponent is 7 why does it make me put 20 charects

Answer:

3

Step-by-step explanation:

27 = 3 to the power of 3

3 x 3 x 3 = 27

What is the value of y?
2y
Y+10
50°

Answers

Answer:

The question is incorrect. Please rewrite the question.

Please Help, 20 points and brainiliest, URGENT.

Answers

Answer:

Step-by-step explanation:

∠ACB and ∠ECD are vertical angles, so ∠ACB = ∠ECD.

∠D = ∠B

∠A = ∠E

△ABC and △EDC are similar because they have the same angles.

A movie theater has a seating capacity of 289. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2106, How many children, students, and adults attended?

Answers

Answer:

Number of children in theater   = 94

Number of students   = 46

Number of adults in theater= 47

Step-by-step explanation:

Total seating capacity in the theater = 187

Let us assume the number of students in the theater = m

and assume  the number of children in the theater = 2k

So, the number of adults in theater = Half of number of children = 2k/2 = k

⇒ Number of ( Adults + Children + students) = 187

⇒ k  + 2k + m =  187, or 3k + m = 187

Step-by-step explanation:

In each bag 1/4 pieces of fruit were raisins. 1/2 were bananas. There were 48 slices of dried banana. The remaining pieces of fruit was raspberries. How many pieces of raisins and dried raspberries were there in each bag

Answers

Half of 48 is 24. So 1/4 of 24 is 12.
You had 12 raisins & 12 raspberries=24
the answer for this problem is 24

Pls help asap!(this question is worth 20 points!)picture down below says question

Answers

Answer:

138

Step-by-step explanation:

c=5

d=4

6c^2-5d+8

substitute c & d

6(5)^2-5(4)+8

6(25)-20+8

150-20+8 = 138

Please answer!!!
y = Yolanda's height in inches
y + 7 = Linda's height in inches
2y + (y + 7) = 193

Answers

193=2y+y+7
193=3y+7
186=3y
62=y
Yolanda is 62 inches tall and Linda is 69 inches tall.

please answer it’s urgent!!

Answers

Area = 64
Perimeter = 16
Area = 64
Perimeter = 32

Area = length x width so 8 x 8 = 64
Perimeter = ALL sides ADDED up together so 8 + 8 + 8 + 8 = 32

bro helppppppppppppp

Answers

Answer:

1. 2 and 2 is c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

1. X+4x+6x need help ASAP 10 minutes remaining ​

Answers

Answer:10x …….….....

Answer:

10x^2 or 10x because you are adding x

Use substitution to solve the linear system of equations.
2y = X - 6
x=9
(9, 24)
(9, 3/2)
(3/2, 9)
(9,9)

Answers

Answer:

2y=X-6

×=9

(9, 3/2)

Step-by-step explanation:

Hope this help!

Answer: 65

Step-by-step explanation: 65

What is the solution to the equation 37x = 9x + 4?

-7

-1/7

1/7

7

Answers

37x = 9x + 4

37x - 9x = 4

28x = 4


x = 7

Answer: The solution is C. 1/7.

Step-by-step explanation: Just plug 1/7 as x. You will find that the statement is true when you plug in 1/7.

7. What is the largest of three consecutive integers whose sum is 39.
A 13
B. 14
C. 17
D. 19

Answers

The answer would be A not 100% sure
Answer: A 13
Expiation: 13 goes into 39 and non others

Need to find the greatest common factor

Answers

Answer: The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers: List the prime factors of each number. Multiply those factors both numbers have in common.

Step-by-step explanation:

Steps to solve 5x +3 = 25x – 2

Answers

Answer: so you have to rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation. There are 3 possible answers x=1

                              x=6

                              x=0

I hope this helps if not I’m rlly sorry.

5x+3 = 25x-2
5x-25x = -2-3
-20x = -5
-20x/-20 = -5/-20
X = 1/4

solve the question 7 _ 2 3/7​

Answers

Answer:

Do you mean 7 - 2 and 3/7?

If so:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Exact Form:

32 /7

Decimal Form:

4. 571428

Mixed Number Form:

4  and 4 /7

Step-by-step explanation:

Have a great day!

Answer:

3.7 the answer.........

Evaluate Square root b2 - 4ac when a = 1, b = -6, and c = 9.

Answers

Answer:

[tex]x=3[/tex]

saben cual es la raiz cuadrada de 3025 con metodo de aproximaciones sucesivas ​

Answers

Answer:

which language is this

5x-7y=58
Y=-x+2
X=
Y=

Answers

Answer:

Since, Y = x + 2

so, 5x-7y = 58

5x-7×x+2 = 58

5x-7x = 58

-2x = 58

x = 58÷2

x = 29

3(6+b)-(2b +1)
Simplify the expression

Answers

the simplified version is b+17

Step-by-step explanation:

3(6+b)-(2b+1)

=18+3b-2b+1

=18+1+3b-2b

=19+b

Select all sports that apply (you may select more than one). The underhand serve is used in...

Badminton
Tennis
Soccer
Pickleball
Voleybal.


Answers

Volleyball, tennis and badminton , I think
Volleyball
Badminton (i believe )

What is the acronym used to help remind you of the order
used to simplify expressions?

Answers

Answer:

I think it's PEMDAS, but I'm not sure- sorry if it's wrong.

Step-by-step explanation:

6.
The distance from London to New York is 3456 miles.
A plane takes 8 hours to fly from London to New York.
Work out the average speed of the plane.
Di

Answers

Answer:

3456/8 = 432

432 miles per hour

Step-by-step explanation:

answer the question below, please

Answers

Answer:

AB = 42.30 m

Step-by-step explanation:

What we are asked to do is to simply find the length of AB.

Since both triangles are similar, therefore their corresponding sides would be proportional to each other.

Thus:

92/82.8 = 47/AB

Cross multiply

92*AB = 82.8*47

92*AB = 3,891.6

AB = 3,891.6/92

AB = 42.30 m(nearest hundredth)

help. everything is in the picture.

Answers

The picture is completely black:/

the picture is completely blank

I need help with this question​

Answers

Answer:

2,540 miles

Step-by-step explanation:

The computation of the fewer miles is given below;

For Space explorer B

= 15,000 miles ÷ 5 hours

= 3,000 miles per hour

For space explorer A

y = 4,600 x

That means in one hour it covered 460 miles

So, the fewer miles would be

= 3,000 - 460

= 2,540 miles

The length of a rectangle is 2 inches more than twice its width. Write an equation relating the length / of the rectangle to its width w.

Answers

Answer:

l = 2w + 2 would be the equation

Find the area of the triangle.
4ft
ift
8ft
[? ] ft2

Answers

there is no triangle attached

Can someone please help me I don’t understand

Answers

Answer:

The ship is traveling at 25 mph

Step-by-step explanation:

12.5/0.5=25

25/1=25

37.5/1.5=25

The speed is constant (25) so the ship is moving at 25 mph

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