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Liono4ka [1.6K]
3 years ago
8

Is a-b parallel to c-d? Explain

Mathematics
1 answer:
Roman55 [17]3 years ago
5 0
Yes both have a line of 3/4
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I need to know the next term in the sequence AND the nth term of all the sequences
ANEK [815]

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

3 0
3 years ago
WILL GIVE BRAINLEST ! <br> hAVE A GOOD DAy :)!
Alina [70]
Is it all like yes or no or does your teacher need like explaining
5 0
3 years ago
A spring coat that cost $60.00 was marked up 20% of the cost. What was the price increase?
Irina18 [472]

The price increase was $12.  

  60

x 0.2  

---------

  12


Hope this helped!

7 0
3 years ago
Read 2 more answers
How to solve -13=5(1 4m)-2m?
Paladinen [302]
First, you would multiply: -13 = 70m - 2m. Then, you subtract the like terms, which would be 70m - 2m: -13 = 68m. You are looking for what m is, so you would divide 68 on both sides: m = - 13 / 68. In math, people would usually like fractions more than decimals, but if you are looking for the decimal number, it would be m ≈ - 0.19.
6 0
3 years ago
Polygon ABCD is dilated, rotated, and translated to form polygon A′B′C′D′. The endpoints of are at (0, -7) and (8, 8), and the e
Alinara [238K]

Answer:

1/2

Step-by-step explanation:

Plato. just had it

5 0
3 years ago
Read 2 more answers
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