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
krek1111 [17]
2 years ago
10

How is the series 5+11+17…+251 represented in summation notation?

Mathematics
1 answer:
NISA [10]2 years ago
5 0

Answer:

\displaystyle \large{\sum_{n=1}^{42}(6n-1)

Step-by-step explanation:

Given:

  • Series 5+11+17+...+251

To find:

  • Summation notation of the given series

Summation Notation:

\displaystyle \large{\sum_{k=1}^n a_k}

Where n is the number of terms and \displaystyle \large{a_k} is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

  • Arithmetic Series

A series that has common difference.

  • Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

  • 11-5 = 6
  • 17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

<u>Arithmetic Sequence</u>

\displaystyle \large{a_n=a_1+(n-1)d}

Where \displaystyle \large{a_n} is the nth term, \displaystyle \large{a_1} is the first term and \displaystyle \large{d} is the common difference:

So for our general term:

\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}

And for number of terms, substitute \displaystyle \large{a_n} = 251 and solve for n:

\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}

Now we can convert the series to summation notation as given the formula above, substitute as we get:

\displaystyle \large{\sum_{n=1}^{42}(6n-1)

You might be interested in
The following examples illustrate the associative property of multiplication.
kati45 [8]

Answer:

A) a • (b • c) = (a • b) • c

Step-by-step explanation:

The associative property of multiplication (or addition) shows that the order the numbers are multiplied it irrelevant, more specifically in the manners of parentheses.

So, the answer is A, which can also be seen in that substituting a as 5, b as 3, and c as 6 gives us the first example.

4 0
2 years ago
Read 2 more answers
Does anyone else agree that the answer for this family of curves question is E, dy/dx = x + y?
neonofarm [45]
Yes this is the correct answer. The slope field shown is the differential equation dy/dx = x+y

All points along the line x+y = k, for some constant k, will have the same tangent slope k. For example, the line x+y = 0 will have every point with tangent slope 0 for the solution y(x). It may not be 100% clear, but this graph has horizontal tickmarks on the line x+y = 0, or the tickmarks are close to being horizontal. Using geogebra, I checked the others and they produced completely different graphs, which allowed me to rule them out.
6 0
3 years ago
PLEASE HELP I’LL MAKE YOU THE BRAINIEST <br> find the area of the trapezoid to the nearest tenth
murzikaleks [220]

Answer:

2.7m

Step-by-step explanation:

1.0m

0.5m

+1.2m

2.7m - answer

5 0
2 years ago
(A) {(-6,2), (3, 4), (4,4), (5, 6)}<br> DOMAIN:<br> RANGE:<br> Is the relation above a function?
vovikov84 [41]

Answer:

Yes

Step-by-step explanation:

Domain: {-6, 3, 4, 5}

Range: {2, 4, 6}

This relation is a function.

6 0
2 years ago
A straight road crosses two parallel railway tracks. The angle between the road and the
Mumz [18]
<h3>Answer:  95 degrees</h3>

=======================================================

Explanation:

I recommend drawing it out to see what's going on. See the drawing below.

In the diagram, both angles are in the northeast corner of their four-corner configurations. They are both congruent corresponding angles. So that's why the second angle is also 95 degrees.

Side note: we could replace "northeast" with any of the other directions on the compass (such as southwest). All that matters is that they are in the same configuration.

7 0
2 years ago
Other questions:
  • The lengths of the perpendiculars drawn to the sides of a regular hexagon from an interior point are 4, 5, 6, 8, 9, and 10 centi
    12·1 answer
  • melissa has 175 pictures to put in her scrapbook. each page holds 8 pictures. How many pages can she fill completely
    5·2 answers
  • What is the length of the hypotenuse of the triangle?
    9·2 answers
  • If the temperature is -4 and rises by 12 degrees what is the new temperature
    5·2 answers
  • a photograph 6 inches wide by 8 inches long is scaled to 12 inches long in a book.what is the width of the published picture?
    14·1 answer
  • Can Someone Plz Help, I have to attachments.
    9·2 answers
  • (3x−2<img src="https://tex.z-dn.net/?f=%29%5E%7B2%7D" id="TexFormula1" title=")^{2}" alt=")^{2}" align="absmiddle" class="latex-
    13·2 answers
  • Please help, I need answers ASAP.......
    8·1 answer
  • PLEASE HELP! OFFERING 20 POINTS, EVEN THOUGH IM RUNNING OUT OF POINTS DUE TO THE AMOUNT OF QUESTIONS I HAVE BEEN ASKING
    15·2 answers
  • Choose the value that will correctly replace the missing part?2(?+5)=6x+10
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!