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
Elenna [48]
3 years ago
9

The 2nd term of an arithmetic progression is (1/2) and the sum of the first 14th terms is -70. Find

Mathematics
1 answer:
Shalnov [3]3 years ago
5 0

Answer:

The common difference is -1.

The last term (the 14th term) is -11.5.

Step-by-step explanation:

In an arithmetic sequence, the second term is 0.5 and the sum of the first 14 terms is -70.

We want to determine the: (a) common difference and (b) the last term.

We can write an explicit formula to represent the sequence. An arithmetic sequence can be modeled by the formula:

\displaystyle x_n=a+d(n-1)

Where <em>a</em> is the initial term, <em>d </em>is the common difference, and <em>n</em> represents the <em>n</em>th term.

Since the second term is 0.5:

x_2=0.5=a+d(2-1)

Simplify:

x_2=0.5=a+d

The sum of an arithmetic sequence is given by the formula:

\displaystyle S=\frac{k}{2}\left(a+x_k\right)

Where <em>k</em> is the number of terms and <em>x_k</em> is the last term.

Since the sum of the first 14 terms is -70, <em>S</em> = -70 and <em>k </em>= 14:

Using our explicit formula, the last term is:

x_{14}=a+d(14-1)=a+13d

Substitute:

\displaystyle -70=\frac{14}{2}(a+(a+13d))

Simplifiy:

-10=2a+13d

Rewrite the equation for the second term:

a=0.5-d

Substitute:

-10=2(0.5-d)+13d

Simplify:

-10=1-2d+13d

Solve for <em>d: </em>

<em />d=-1<em />

Hence, our common difference is -1.

Solve for <em>a</em>, the initial term:

a=0.5-(-1)=1.5

So, our explicit formula is now:

x_n=1.5-1(n-1)=1.5-n+1=2.5-n

So, the last term (which is 14) is:

x_{14}=2.5-(14)=-11.5

You might be interested in
Sean has to face a big problem but he becomes stronger as a result which saying best summarizes the change in Sean?
kkurt [141]

Answer: D. every cloud has a silver lining

The cloud represents a dark, scary, or sad moment. This is in contrast to the sun which metaphorically represents energy and happiness. The cloud sometimes covers up the sun to cover up those happy moments so to speak.

Despite the cloud being present, there's a silver lining to the cloud which represents some positive aspect a person didn't expect to happen. In this case, the problem allows Sean to get stronger. So this is an opportunity for his growth.

7 0
3 years ago
Find the distance between the two points:<br> (-16,5) and (3,5)
egoroff_w [7]

The distance is 19

Hope this helps! :D

4 0
3 years ago
Read 2 more answers
.<br> 2. Find the volume of the right cone.<br> 4 cm<br> 3 cm
Ainat [17]

Answer:

i dont get it please alaborate

Step-by-step explanation:

4 0
3 years ago
What percentage of the data values represented on a box plot falls between the minimum value and the lower quartile?
Butoxors [25]

Answer:

first 25%

Step-by-step explanation:

A quartile is a quarter, so the first 25% falls between the minimum and lower quartile

4 0
3 years ago
Read 2 more answers
Liam is setting up folding chairs for a meeting. If he arranges the ch
marishachu [46]

Answer:

Step-by-step explanation:

This is the answer

8 0
3 years ago
Other questions:
  • Felix Carson is employed at a high school. He has family medical coverage through the school's
    5·1 answer
  • I don’t understand how to set up the equation and expressions, I pretty much need help with everything
    13·2 answers
  • Completely factor the polynomial. 16x 2 - 25
    11·1 answer
  • Someone please help!! i will<br> make you a brainliest...i don’t want to fail:(((
    8·1 answer
  • Solve for x<br><br> Help me please
    10·1 answer
  • Can you explain plz help
    9·1 answer
  • A mayor estimates that 4,000 people will attend
    8·2 answers
  • Thank you for the help
    12·1 answer
  • What is the ratio of the two quantities? Warning: different units!
    6·2 answers
  • Could the solutions of a system of inequalities be a rectangular region? If so, give an example.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!