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
bulgar [2K]
2 years ago
7

I need to know the next term in the sequence AND the nth term of all the sequences

Mathematics
1 answer:
ANEK [815]2 years ago
3 0

I see you already did the ones where you figured out the formula.  There's a fun way that doesn't require figuring out the formula, called a forward difference table.

Let's work out the first one to learn the technique.  We write the sequence and under it the forward differences,

2 5 10 17 26

3 5  7  9

2 2 2  

We got 3=5-2, 5=10-5, 7=17-10, etc and the same for subsequent lines.  Eventually we get to an all constant line and we stop.

To extend the table we just add some constants to the constant line and work our way back up:

2 5 10 17 26 37 50

3 5  7  9  11  13

2 2 2   2  2

So we get 11 as 9+2 and 37 as 26+11 for our answer which matches the answer you already got.

Let's do the ones you haven't.

2 8  18 32 50 72

6 10 14 18  22

4  4  4   4  

Answer: 72

3 9  19  33 51   73

6 10 14  18  22

4 4  4    4

Answer: 73

2 11 26 47 74  107

9 15 21 27  33

6 6  6    6

Answer: 107

Three's our limit so I'll leave the last one to you.

---

A comment says we need the functions.  They're all quadratics.  I'll tell you how they want you to do it and how to do it in general.

They just want you to recognize these are all pretty close to just u_n=n^2.   The one that goes 3 12 27 etc. we recognize as just u_n=3n^2.   The one that goes 2 8 18 is just u_n =2n^2.  The one that goes 3 9 19 is one more than that so u_n=2n^2+1. The one that goes 2 11 26... is one less than 3 12 27 so is u_n=3n^2-1.  Again I'll leave the last one.

----

We can do these quadratics in general.  Let's work from our difference table.  If we have

f(n) = an^2 + bn + c

and we form the difference table for f(1), f(2), f(3) we get

a+b+c   4a+2b+c   9a+3b+c

3a+b     5a+b

2a

so we can use the first columns of our difference tables to get our polynomial.  

2 8  18 32 50 72

6 10 14 18  22

4  4  4   4  

Answer: 72

So we have 2a=4, so a=2

3a+b=6, so b=6-3(2)=0

a+b+c=2 so c=2-0-2=0

That gives us the obvious answer

u_n = 2n^2

3 9  19  33 51   73

6 10 14  18  22

4 4  4    4

Answer: 73

We have 2a=4 again so a=2, 3a+b=2 so b=0, and a+b+c=3 so c=1 giving

u_n = 2n^2+1

2 11 26 47 74  107

9 15 21 27  33

6 6  6    6

Answer: 107

2a=6 gives a=3

3a+b=9 gives b=0

a+b+c=2 gives c= -1

u_n = 3n^2-1

You might be interested in
When calculating total savings you must
Art [367]
Subtract 10 evertime cuz that s taxes
5 0
3 years ago
Read 2 more answers
What quadrilateral have all the attributes of rhombus ​
marusya05 [52]

Answer:

A rhombus and a square since a square is also a rhombus.

8 0
3 years ago
Please help with this!!
maw [93]

Answer:

gcf=2

12-2=4(3-1)

hope this is right!

8 0
2 years ago
write a word problem that can be solved using multiplication of two-digit numbers.Solve your word problem explain the solution.
andrew11 [14]
____ was planning a birthday party. He/she is planning on inviting 14 people to the party. Each person will be given a goodie-bag at the end of the party. ____ decided that he/she will put 19 gummy worms into each bag. how many gummy worms will ____ need?

The answer to this problem is 266 because 14x19= 266.

the person needs 266 gummy worms if they want to put 19 into each person's goodie-bag
4 0
2 years ago
Read 2 more answers
Simplify (x^-5) (x^2)*​
Pani-rosa [81]

Answer:

1/x^3

Step-by-step explanation:

foil method

6 0
3 years ago
Other questions:
  • Dave Adams bought season tickets for the Boston Celtics. The cost was $1,300.11. The package included 30 home games. What is the
    11·1 answer
  • I need help finds my the answer
    13·1 answer
  • Simplify the expression. What classification describes the resulting polynomial?
    9·2 answers
  • Find the area of the hexagen whose Vertices taken in order
    10·1 answer
  • Pls I need help pls​
    8·1 answer
  • Which inequality is true if p = 3.4? A. 3p < 10.2 B. 13.6 < 3.9p C. 5p > 17.1 D. 8.5 > 2.5p
    10·1 answer
  • Someone please help me its due today plesse!!!❤​
    6·1 answer
  • Is 9,783,005 divisible by 3?
    5·1 answer
  • 412/47 as a mixed number
    11·1 answer
  • What is the probability of picking a blue marble and flipping heads?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!