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
nlexa [21]
2 years ago
6

Activity 4: Performance Task

Mathematics
2 answers:
Nookie1986 [14]2 years ago
4 0

An arithmetic progression is simply a progression with a common difference among consecutive terms.

  • <em>The sum of multiplies of 6 between 8 and 70 is 390</em>
  • <em>The sum of multiplies of 5 between 12 and 92 is 840</em>
  • <em>The sum of multiplies of 3 between 1 and 50 is 408</em>
  • <em>The sum of multiplies of 11 between 10 and 122 is 726</em>
  • <em>The sum of multiplies of 9 between 25 and 100 is 567</em>
  • <em>The sum of the first 20 terms is 630</em>
  • <em>The sum of the first 15 terms is 480</em>
  • <em>The sum of the first 32 terms is 3136</em>
  • <em>The sum of the first 27 terms is -486</em>
  • <em>The sum of the first 51 terms is 2193</em>

<em />

<u>(a) Sum of multiples of 6, between 8 and 70</u>

There are 10 multiples of 6 between 8 and 70, and the first of them is 12.

This means that:

\mathbf{a = 12}

\mathbf{n = 10}

\mathbf{d = 6}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{10} = \frac{10}2(2*12 + (10 - 1)6)}

\mathbf{S_{10} = 390}

<u>(b) Multiples of 5 between 12 and 92</u>

There are 16 multiples of 5 between 12 and 92, and the first of them is 15.

This means that:

\mathbf{a = 15}

\mathbf{n = 16}

\mathbf{d = 5}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{16} = \frac{16}2(2*15 + (16 - 1)5)}

\mathbf{S_{16} = 840}

<u>(c) Multiples of 3 between 1 and 50</u>

There are 16 multiples of 3 between 1 and 50, and the first of them is 3.

This means that:

\mathbf{a = 3}

\mathbf{n = 16}

\mathbf{d = 3}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{16} = \frac{16}2(2*3 + (16 - 1)3)}

\mathbf{S_{16} = 408}

<u>(d) Multiples of 11 between 10 and 122</u>

There are 11 multiples of 11 between 10 and 122, and the first of them is 11.

This means that:

\mathbf{a = 11}

\mathbf{n = 11}

\mathbf{d = 11}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{16} = \frac{11}2(2*11 + (11 - 1)11)}

\mathbf{S_{11} = 726}

<u />

<u>(e) Multiples of 9 between 25 and 100</u>

There are 9 multiples of 9 between 25 and 100, and the first of them is 27.

This means that:

\mathbf{a = 27}

\mathbf{n = 9}

\mathbf{d = 9}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{9} = \frac{9}2(2*27 + (9 - 1)9)}

\mathbf{S_{9} = 567}

<u>(f) Sum of first 20 terms</u>

The given parameters are:

\mathbf{a = 3}

\mathbf{d = 3}

\mathbf{n = 20}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{20} = \frac{20}2(2*3 + (20 - 1)3)}

\mathbf{S_{20} = 630}

<u>(f) Sum of first 15 terms</u>

The given parameters are:

\mathbf{a = 4}

\mathbf{d = 4}

\mathbf{n = 15}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{15} = \frac{15}2(2*4 + (15 - 1)4)}

\mathbf{S_{15} = 480}

<u>(g) Sum of first 32 terms</u>

The given parameters are:

\mathbf{a = 5}

\mathbf{d = 6}

\mathbf{n = 32}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{32} = \frac{32}2(2*5 + (32 - 1)6)}

\mathbf{S_{32} = 3136}

<u>(g) Sum of first 27 terms</u>

The given parameters are:

\mathbf{a = 8}

\mathbf{d = -2}

\mathbf{n = 27}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{27} = \frac{27}2(2*8 + (27 - 1)*-2)}

\mathbf{S_{27} = -486}

<u>(h) Sum of first 51 terms</u>

The given parameters are:

\mathbf{a = -7}

\mathbf{d = 2}

\mathbf{n = 51}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{51} = \frac{51}2(2*-7 + (51 - 1)*2)}

\mathbf{S_{51} = 2193}

Read more about arithmetic progressions at:

brainly.com/question/13989292

mariarad [96]2 years ago
4 0

Answer:

photosynthesis is a processes by which plants get their proteins

You might be interested in
I REALLY NEED HELP ON THESE TWO QUESTIONS!!! I'd really appreciate it...
Mariana [72]

Answer:

On the first one the total is 37500.The second dealer is again,37500.You put a coma after every 3 digit so the coma is 357,000.Sorry if I over explained it.

6 0
3 years ago
Read 2 more answers
Plss answer my question now i need it this friday​
professor190 [17]
Hello! i can do the first word problem

first we need to divide 600/3 which is 200.
therefore we can infer that he does 200 letters an hour and we can solve the problem with this

200 x 7 = 1400 letters an hour
6 0
3 years ago
Simplify this expression 9xy4x 3x3y​
Alekssandra [29.7K]

Answer:

81 x y^5

Step-by-step explanation:

Simplify the following:

9×3×3 x y^4 y

3×3 = 9:

9×9 x y^4 y

9 x y^4×9 y = 9×9 x y^(4 + 1):

9×9 x y^(4 + 1)

4 + 1 = 5:

9×9 x y^5

9×9 = 81:

Answer: 81 x y^5

7 0
3 years ago
What is the measure of an angle that is it’s own complement ?
ValentinkaMS [17]

A complement is angle that can be added to another to equal 90 degrees.

So two times the same number would equal 90.

90 / 2 = 45

The angle that is its own complement is 45 degrees.

8 0
3 years ago
A track has the shapes shown. what is the perimeter ?
USPshnik [31]
Break this problem down first. You have two lines each with length of 5. You also have two halves of a circle, combine them to get a full circle with a radius of 2. The formula to find the perimeter of a circle is
2\pi \times r
and this gives a perimeter of 12.566 for the circle. Add this to your sides and you get a total of 22.566 which is answer B
4 0
3 years ago
Other questions:
  • at a sale search were sold for $15 each. This price was 80% of the original price. What was the original price?
    14·2 answers
  • The five values for a data set are: minimum = 0 lower quartile = 2 median = 3.5 upper quartile = 5 maximum = 10 Bruno created th
    15·2 answers
  • What is 1/11 + 2/11 simplified
    7·2 answers
  • There are 8 feet and 4 heads in Ms. Wilson’s class. If 4 feet belong to boys and 4 feet belong to girls, what is the ratio of bo
    8·1 answer
  • A group of two friends each received six-twelfths of a pound of candy. How much candy did they receive total?
    11·2 answers
  • What is the simplified form of this equation f(x)=<br>x2 + 4x + 10​
    8·2 answers
  • Y = -3x + 10<br> Y = -2x + 6<br><br> The solution to this system is ( ? , ? )
    7·1 answer
  • Which of the rectangular boxes shown has the greater volume?
    7·1 answer
  • Atasha jumped 2 1/5 meter in a long jump competition. Arya jumped 1 2/3 meter. Who jumped longer and how many meters?​
    10·1 answer
  • What is the median of the 19 numbersplotted in the line plot below?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!