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
Ksivusya [100]
2 years ago
10

A) If the 5th term of an A.P. is double the 7th term, show that the sum of the 17 terms zero.​

Mathematics
1 answer:
gayaneshka [121]2 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

The nth term of an AP is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₅ is double a₇ , then

a₁ + 4d = 2(a₁ + 6d) , that is

a₁ + 4d = 2a₁ + 12d ( subtract a₁ from both sides )

4d = a₁ + 12d ( subtract 12d from both sides )

- 8d = a₁

The sum of n terms of an AP is

S_{n} = \frac{n}{2} [ 2a₁ + (n - 1)d ] , substitute values

S_{17} = \frac{17}{2} ( 2(- 8d) + 16d)

     = 8.5(- 16d + 16d)

     = 8.5 × 0

     = 0

You might be interested in
How do I Simplify 4a – 7b + 2ab – a + b (I need step by step cause I'm trying to learn this)
Alex

Step-by-step explanation:

Ok. First of all, we need to follow the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. We don't have any parentheses, exponents, or division to resolve, so you can skip those. So now you have: Multiplication, Addition, and Subtraction. We have multiplication in each term, but each term is fully simplified, so we have Addition and Subtraction left.

With that out of the way, let's go ahead and rearrange this equation so it is easier to solve. (<em>Note: we can only rearrange terms that are positive because subtraction is not commutative. But we can turn negative terms into "positive" terms by the method shown below.</em>)

4a - 7b + 2ab - a + b

4a + (-7b) + 2ab + (-a) + b (<em>Now the terms are all positive, so we can rearrange them, but they still have the same value.</em>)

4a + (-a) + 2ab + (-7b) + b

3a + 2ab + 7b

And there we go. Our answer is fully simplified. If you can understand this, you'll be able to simplify without isolating and rearranging the terms each time.

Hopefully this was helpful and not confusing.

4 0
3 years ago
The faces of a triangular pyramid have a base of 5 cm and height of 11 cm. What is the lateral area of the pyramid?
horrorfan [7]
I think 55 because you would multiply 11×5
7 0
3 years ago
Use the multiplier method to decrease £27 by 8%. You must show your working.
Nitella [24]

Answer:

decrease by 2.16

Step-by-step explanation:

Convert the problem to an equation using the percentage formula: P% * X = Y.

P is 10%, X is 150, so the equation is 10% * 150 = Y.

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.

3 0
3 years ago
Read 2 more answers
Find the slope of each line. <br> 2
ratelena [41]

Answer: m=3/2

Step-by-step explanation: the slope starts from the left side and the line is going up meaning its positive, now the line is going up by 3s and to the right in 2s.

5 0
3 years ago
3-3x6+2 and how is that reached, please!
Dvinal [7]
The order of mathematical operation is MDAS.
M - multiplication
D - division
A - addition
S - subtraction

3 - 3 x 6 + 2

Multiplication : 3 x 6 = 18
Division: none
Addition : + 3 + 2 = 5 (combine positive numbers)
Subtraction : 5 - 18 = -13

3 - 18 + 2 = -13
3 0
3 years ago
Other questions:
  • A large school district is considering moving up the start date for the school year by two weeks. In order to determine if famil
    9·1 answer
  • When multiplying 2 fractions is the product greater than the factors?
    14·1 answer
  • Andrew makes 11 saves in 2 soccer games. He made 8 saves in the first game. How many saves did Andrew make in the second game?
    7·2 answers
  • Milk is being poured into a cylindrical pail at a constant rate of 8 cubic inches per second. The pail has a base radius of 5 in
    12·1 answer
  • Y varies jointly as x and z z. If y = 6 when x = 3 and z = 9, find y when x = 4 and z = 3.6.
    11·1 answer
  • Answer 7 and 8 2 questions for brainliest answers UGRENT HELP NOW!!!!!
    11·2 answers
  • Simplify pleasee it’s urgent : 8f+5f-f
    8·2 answers
  • Rewrite each equation in standard form<br> Y=6x-4
    9·1 answer
  • 3<br> y=-=X+2<br> 4.<br> What is the slope
    8·1 answer
  • Help please 75 points and brainliest
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!