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
kobusy [5.1K]
2 years ago
10

Evaluate arithmetic series:- Step-by-step answer, please!

Mathematics
2 answers:
VladimirAG [237]2 years ago
8 0

Answer:

-186,450

Step-by-step explanation:

<u>Sum of arithmetic series formula</u>

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

where:

  • a is the first term
  • d is the common difference between the terms
  • n is the total number of terms in the sequence

\displaystyle \sum\limits_{k=1}^{275} (-5k+12)

To find the first term, substitute k = 1 into (-5k+12)

a_1=-5(1)+12=7

To find the common difference, find a_2 then subtract a_1 from a_2:

a_2=-5(2)+12=2

\begin{aligned}d & =a_2-a_1\\ & =2-7\\ & =-5\end{aligned}

Given:

  • a=7
  • d=-5
  • n=275

\begin{aligned}S_{275} & = \dfrac{275}{2}[2(7)+(275-1)(-5)]\\& = \dfrac{275}{2}[14-1370]\\& = \dfrac{275}{2}[-1356]\\& = -186450\end{aligned}

lorasvet [3.4K]2 years ago
4 0

Let's see

\\ \rm\Rrightarrow {\displaystyle{\sum^{275}_{k=1}}}(-5k+12)

\\ \rm\Rrightarrow (-5(1)+12)+(-5(2)+12)\dots (-5(275)+12)

\\ \rm\Rrightarrow 7+5+3+2+1+\dots -1363

So

  • a=7
  • l=-1363
  • n=275

Sum:-

\\ \rm\Rrightarrow S_n=\dfrac{n}{2}[a+l]

\\ \rm\Rrightarrow \dfrac{275}{2}(7-1363)

\\ \rm\Rrightarrow \dfrac{275}{2}(-1356)

\\ \rm\Rrightarrow 275(-678)

\\ \rm\Rrightarrow -186450

You might be interested in
Please help me with this math problem I don’t know it I need to pass this class !!!!!!
Alisiya [41]

The correct option is Option 4: 2a^2b^3 + 10ab^4

Step-by-step explanation:

Given

Length of box = l = ab

Width of box = w = a+5b

Height of box = h = 2b^2

The volume of a box is given by:

V = Length*Width*Height\\V = l*w*h

Putting the values

V = (ab)(a+5b)(2b^2)\\ = (ab)(2b^2)(a+5b)\\=(2ab^3)(a+5b)\\Distributive property\\=(2ab^3*a) + (2ab^3*5b)\\=2a^2b^3 + 10ab^4

Hence,

The correct option is Option 4: 2a^2b^3 + 10ab^4

Keywords: Volume, Polynomials

Learn more about polynomials at:

  • brainly.com/question/9103248
  • brainly.com/question/9323337

#LearnwithBrainly

4 0
3 years ago
The number 9 has only 1 prime factor, 3. What is another number less than 50 only 1 prime factor?
tino4ka555 [31]

Answer:

15

Step-by-step explanation:

There is 15. 5x3=15, and no others factors would work!

7 0
3 years ago
Read 2 more answers
Currently, Nora is 3 time as old as damon. In 8 years she will be only 2 time as old as Damon. How old will Damon will be in 8 y
Ann [662]

In 8 years Damon will be 16 year's old.

We have Nora who 3 time as old as Damon and in 8 years she will be only 2 time as old as Damon.

We have to determine how old will Damon  be in 8 years.

<h3>If your present age is x and your sister is 4 years elder than you. Than what will be her age after 5 years from now.</h3>

Your present age = x.

Hence, your sister's present age = x + 4.

After five years, your age = x + 5.

Hence, your sister's age will be = x + 9.

According to question, we have -

Assume that the present age of Damon is x.

Then, Nora's age will be = y = 3x.

After 8 years -

Damon's age = x + 8

Nora's age = 3x + 8

Therefore -

3x + 8 = 2(x + 8)

3x + 8 = 2x + 16

x = 8

Hence, in 8 years Damon will be = 8 + 8 = 16 year's old.

To solve more questions on Age determination, visit the link below -

brainly.com/question/14580151

#SPJ1

6 0
1 year ago
Use substitution to determine if the solution is correct (PINK HIGHLIGHTED ONE!!!)
mart [117]

Answer:

It is not correct.

Step-by-step explanation:

If you plug 4 in for x, you get -2*4+5=13. This simplifies to: -8+5=13. This is an untrue statement since -8+5 is actually -3, not 13.

Hope this is helpful! :)

4 0
3 years ago
Read 2 more answers
Saved
Scorpion4ik [409]
Answer: 91/167

Explanation:
7 0
3 years ago
Other questions:
  • Which function has the largest slope? A) y = 4x + 5 B) y = 3x + 25 C) y = 8x + 2 4 D) A function showing a rock collection growi
    13·2 answers
  • the domain of the function f(x) = 3x3 is {2, 5}. what is the function’s range? the range of the function f(x) = 3x3 when its dom
    13·2 answers
  • The sum of these consecutive integers is equal to 9 less than 4 times the least of the integer. Find the three integers
    6·1 answer
  • A fair 6-sided die is rolled 4 times and the resulting sequence of 4 numbers is recorded. How many different sequences consist e
    12·1 answer
  • Find the area of rectangle 7 cm long 3 cm wide give a unit of measurement
    5·2 answers
  • Please help me due today i beg of u
    13·2 answers
  • NEED HELP ASAP MAKE SURE RIGHT ANSWER
    11·2 answers
  • 3.1.PS-20
    8·1 answer
  • Can some on help me please
    6·1 answer
  • Darnell buys homes and flips them by completing renovations to turn a profit on his investment. He is currently working on a hou
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!