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
Blue River is 212 miles long. What is the length of the river on the map, if the scale is 1 inch : 50 miles?
exis [7]
Answer: 4.24 inches
Explanation: divide 212 by 50
5 0
2 years ago
What is the proportion for x
Artist 52 [7]
12x15=18(3x+4)
180=54x+72
-72 -72
108=54x
/54 /54
2=x

X=2 the other person is a d0uche for answering like that so I answered instead of them
8 0
3 years ago
Y = 3x<br> x + y = 52<br><br> substitution method <br> help quick <br> show all work
AfilCa [17]

Answer:

x + 3x = 52 \\ 4x = 52 \\ x = 13 \\ y = 3x = 3 \times 13 = 39

8 0
2 years ago
P(x)=(x-2)(x-4)(x-5)
Cerrena [4.2K]

The constants of a polynomial is the term that has no variable attached to it.

<h3>The constant term</h3>

To determine the constant, we simply multiply the constant term in each factor of the polynomial.

So, we have:

<h3 /><h3>Polynomial P(x) = (x-2)(x-4)(x-5)</h3>

Constant = -2 \times -4 \times -5

Constant = -40

Hence, the constant is -40

<h3>Polynomial P(x) = (x-2)(x-4)(x+5)</h3>

Constant = -2 \times -4 \times 5

Constant = 40

Hence, the constant is 40

<h3>Polynomial P(x) =1/2(x-2)(x-4)(x+5)</h3>

Constant = \frac 12 \times -2 \times -4 \times 5

Constant = 20

Hence, the constant is 20

<h3>Polynomial P(x) = 5(x-2)(x-4)(x+5)</h3>

Constant = 5 \times -2 \times -4 \times 5

Constant = 200

Hence, the constant is 200

<u>P(x) =-5(x-2)(x-4)(x+5)</u>

Constant = -5 \times -2 \times -4 \times 5

Constant = -200

Hence, the constant is -200

Read more about polynomials at:

brainly.com/question/2833285

5 0
2 years ago
Match each whole number with a rational, exponential expression.
Katyanochek1 [597]

1.\\9=3^2\\2.\\196=14^2\\3.\\256=16^2=4^4=2^8\\4.\\225=15^2\\5.\\16=4^2=2^4\\6.\\25=5^2

4 0
2 years ago
Other questions:
  • -0.75-(-2/5)+0.4+(-3/4)
    10·1 answer
  • Help me with Question #11. Also can you correct questions #1-10
    7·2 answers
  • Write the equation for g(x).
    5·1 answer
  • -0.113 blank =0.452x + 0.452
    7·1 answer
  • 3x+5=19 how do I solve this problem ???
    7·2 answers
  • Jason took a taxi from his home to the airport. <br> the taxi driver charged an initial fee of $12
    8·1 answer
  • A circle has a circumference of 16 7 feet. What is the<br> radius of the circle, in feet?
    8·1 answer
  • Calculate the area of the shape below.
    13·1 answer
  • Kara wants to make a histogram of the number of students who wear blue shirts in her class throughout the week. She gathered the
    5·1 answer
  • How many helmets must the company make and sell to break even? helmets
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!