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
gulaghasi [49]
2 years ago
6

Someone please help me on both the questions!!!

Mathematics
2 answers:
bonufazy [111]2 years ago
7 0

Step-by-step explanation:

al nth term:

numerator:

=  {n}^{2}

denominator:

= n + 1

so nth term :

=  \frac{ {n}^{2} }{n + 1}

b). 1; 11; 27; 49

first difference: 10; 16; 22

second difference :6

formula for 1st difference:3a+b

formula for 2nd difference:2a

Therefore:

2a=6

a=3

3a+b=10

sub in a

3(3)+b=10

9+b=10

b=1

sub into quadratic formula

{an}^{2}  + bn  + c

(3) {(1)}^{2}  + (1)(1) + c = 1

3(1) + 1 + c = 1

3 + 1 + c = 1

4 + c = 1

c  = - 3

So Tn:

3 {n }^{2}  +  1n - 3

Pavel [41]2 years ago
3 0

Step-by-step explanation:

a)

it is clearly a sequence of the square numbers over the numbers+1.

1/2 = 1²/(1+1)

4/3 = 2²/(2+1)

9/4 = 3²/(3+1)

16/5 = 4²/(4+1)

so, the nth term would be

n²/(n+1)

b)

an² + bn + c creates the sequence with increasing n (n = 1, 2, 3, 4, ...)

since for sequence the first starting value is often not generated by the general expression, we have to focus on n = 2, n = 3 and n = 4, and with that we get 3 equations with 3 variables (a, b, c) that we can solve :

n = 2

a×2² + b×2 + c = 11 = 4a + 2b + c

n = 3

a×3² + b×3 + c = 27 = 9a + 3b + c

n = 4

a×4² + b×4 + c = 49 = 16a + 4b + c

the first equation gives us

c = 11 - 4a - 2b

when we use this in the second equation, we get

27 = 9a + 3b + 11 - 4a - 2b = 5a + b + 11

b = 16 - 5a

now we use both of that in the third equation :

49 = 16a +4(16 - 5a) + 11 - 4a - 2(16 - 5a) =

= 16a + 64 - 20a + 11 - 4a - 32 + 10a =

= 2a + 43

2a = 6

a = 3

b = 16 - 5a = 16 - 5×3 = 16 - 15 = 1

c = 11 - 4a - 2b = 11 - 4×3 - 2×1 = 11 - 12 - 2 = -3

You might be interested in
Write an algebraic expression for the following: twice a number *
Sliva [168]
2x ! the number would be x and 2x is 2 times x!
4 0
2 years ago
Read 2 more answers
*Reminder: If you have not filled out your graphic organizer to reflect the order of events in Part I of "The Monkey's
Andrew [12]

The two events that created the most tension in the story include:

  • Mrs. White suggests that her husband wishes for four hands for her.
  • Mr. White paid Sergeant-Major Morris a trifle for the paw.

<h3>What is tension?</h3>

It should be noted that tension in literature simply means the sense of something ominous in the literary work. It's a feeling that something is about to happen.

The Monkey's Paw is a horror short story by author W. W. Jacobs. In the story, three wishes are granted to the owner of The Monkey's Paw, but the wishes come with a price for interfering with fate.

It should be noted that Mrs. White suggesting that her husband wish for four hands for her created tension in the story as the readers were eager to know what happened in the story. Also, it should be noted Mr. White paying Sergeant-Major Morris a trifle for the paw created tension.

Learn more about tension on:

brainly.com/question/918617

#SPJ1

8 0
1 year ago
Pedestrian or bicycle $0.50
Zielflug [23.3K]
2 groups if 4 bicyclists or 4 groups of 2 bicyclists. Well it's only 1.75 per truck so since there were 4 trucks 4•1.75=7.00 :)
5 0
2 years ago
I need help on this
Evgen [1.6K]

Answer:

the last one talking about victoria has y dollars

Step-by-step explanation:

x times 12 is equal to y, so the equation is y = 12x

6 0
2 years ago
Read 2 more answers
Cho S là ngoại diên của khái niệm con người, p(x,y) = x yêu thương y.
pentagon [3]

Answer:

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • Which best describes the range of the function f(x) = 2/3(6)x after it has been reflected over the x-axis?
    9·2 answers
  • Show your work:
    11·1 answer
  • Help Math All the Points i have
    8·1 answer
  • I need help bad this is so hard i don't know what to do
    9·1 answer
  • If point T was located at 4,6 and moved 3 units to the left and 2 units down, at what coordinations will point T be located
    15·1 answer
  • What is 0.875 simplest form
    6·2 answers
  • Dustin rides his bike for 176.25 miles in three weeks. He averaged 11.75 miles per hour each time he rode. How many hours did it
    8·1 answer
  • Need help plz I need to pass this.
    11·2 answers
  • If k is a constant, what is the value of k such that the polynomial 2ky^-kx-8 is divisible by (x-2)
    13·2 answers
  • Lilly uses 9 flowers in each bouquet. She needs flowers for at most 18 bouquets. Determine how many flowers Lilly needs for the
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!