Maths Formulas Watch

Michael12341234
Badges: 2
Rep:
?
#1
Report Thread starter 13 years ago
#1
..
0
quote
reply
Neapolitan
Badges: 1
Rep:
?
#2
Report 13 years ago
#2
(Original post by alexsmithson)
Hi, does anyone know what the formulas are to these sequences?

1] 14,25,37,50,64
2] 22,34,46,58,70
3] 7,17,28,40,53
4] 17,29,42,56
5] 2,7,14
6] 2,6,11,17,24
7] 3,8,15,24,35
8] 17,24,31,38,45

I will give positive rep to anyone that can help.

Thanks in advance, Alex.
Look at the differences between consecutive terms.

These questions are always a little absurd as there are infinitely many formulae that would work. #5, with only three terms, is especially daft.
0
quote
reply
Neapolitan
Badges: 1
Rep:
?
#3
Report 13 years ago
#3
(Original post by alexsmithson)
Do you know the answers though?

Thanks, Alex.
Surely you can work them out once you note the pattern in the differences. When the differences are no worse than linear then the terms themselves will be no worse than quadratic.
0
quote
reply
Simba
Badges: 15
Rep:
?
#4
Report 13 years ago
#4
1] 14,25,37,50,64
2] 22,34,46,58,70
3] 7,17,28,40,53
4] 17,29,42,56
5] 2,7,14
6] 2,6,11,17,24
7] 3,8,15,24,35
8] 17,24,31,38,45
2) 12n + 10
5) n² + 2n - 1
8) 7n + 10

Try searching 'sequences and series' or something like that on google, I'm sure you'll be able to find out something about the method of differences ...

Hope this helps,

~~Simba
0
quote
reply
meathead
Badges: 5
Rep:
?
#5
Report 13 years ago
#5
(Original post by alexsmithson)
Hi, does anyone know what the formulas are to these sequences?

1] 14,25,37,50,64
2] 22,34,46,58,70
3] 7,17,28,40,53
4] 17,29,42,56
5] 2,7,14
6] 2,6,11,17,24
7] 3,8,15,24,35
8] 17,24,31,38,45

I will give positive rep to anyone that can help.

Thanks in advance, Alex.
1] 14,25,37,50,64
Differences: 11, 12, 13, 14..

differences are linear, so our function will be quadratic.

let tn = an² + bn + c

n = 0: t0 = c = 14.
n = 1: t1 = a + b + c = 25
n = 2: t2 = 4a + 2b + c = 37

a+b = 11
4a+2b = 23
2a = 1 -> a = ½ -> b = 10½

tn = ½(n² + 21n + 28)

2] 22,34,46,58,70
differences: 12, 12, 12 ,12

tn = 22 + 12n.


3] 7,17,28,40,53
differences: 10, 11, 12, 13
note the differences increase at the same rate as in 1], so we can cheat.
let a = sequence from Q1, b = sequence from this question.
b0 = a0 - 7.
b1 = a1 - 8.
b2 = a2 - 9.
b3 = a3 - 10 ...

bn = an - 7 - n.
= ½(n² + 21n + 28) - 7 - n = ½(n² + 19n + 14)

4] 17,29,42,56
differences:
12,13,14.

same method as 3], answer is:
tn = ½(n² + 23n + 34)


5] 2,7,14
This one really is a bit short. One idea is 2x7 = 14, and tn+2 = tn * tn+1. This will give you tn = 2^(Fn-2) * 7^(Fn-1) for n >= 2 (Fn is the nth fibonacci number). I don't think that's what they are looking for , so just assume it's like 1]...

n = 0: t0 = c = 2.
n = 1: t1 = a + b + c = 7
n = 2: t2 = 4a + 2b + c = 14

a + b = 5.
4a + 2b = 12.
-> 2a = 2.
-> a = 1,b = 4,c=2.

tn = n² + 4n + 2

6] 2,6,11,17,24
dif: 4,5,6,7

tn = ½(n² + 7n + 4)


7] 3,8,15,24,35
dif: 5,7,9,11

tn = n² + 4n + 3

8] 17,24,31,38,45
dif: 7,7,7,7

tn = 17 + 7n
0
quote
reply
Simba
Badges: 15
Rep:
?
#6
Report 13 years ago
#6
Meathead has the right idea, but as far as I'm aware at GCSE level at least, and up to where I am at A-level, it's normal to start with t1 than t0.

So, both mine and Meathead's solutions are correct ...
0
quote
reply
Chewwy
Badges: 15
Rep:
?
#7
Report 13 years ago
#7
(Original post by alexsmithson)
So far, I have got these.

1] 14,25,37,50,64-----=-----½(n²+21n+28) ----->is there any way to make this smaller?
2] 22,34,46,58,70-----=-----12n+10
3] 7,17,28,40,53-------=-----½(n²+19n+14) ----->is there any way to make this smaller?
4] 17,29,42,56---------=-----½(n²+23n+34) ----->isthere any way to make this smaller?
5] 2,7,14---------------=-----n²+2n-1
6] 2,6,11,17,24--------=-----½(n²+7n+4) ----->is there any way to make this smaller?
7] 3,8,15,24,35--------=-----n²+2n
8] 17,24,31,38,45-----=-----7n+10

Just wanted to make them all in the same form. Can it be done?

Thanks again, Alex.
they are of the same form - quadratics. just some of the coefficients are fractions.
0
quote
reply
damaster275
Badges: 1
Rep:
?
#8
Report 13 years ago
#8
(Original post by alexsmithson)
So far, I have got these.

1] 14,25,37,50,64-----=-----½(n²+21n+28) ----->is there any way to make this formula smaller?
2] 22,34,46,58,70-----=-----12n+10
3] 7,17,28,40,53-------=-----½(n²+19n+14) ----->is there any way to make this formula smaller?
4] 17,29,42,56---------=-----½(n²+23n+34) ----->isthere any way to make this formula smaller?
5] 2,7,14---------------=-----n²+2n-1
6] 2,6,11,17,24--------=-----½(n²+7n+4) ----->is there any way to make this formula smaller?
7] 3,8,15,24,35--------=-----n²+2n
8] 17,24,31,38,45-----=-----7n+10

Just wanted to make them all in the same form. Can it be done?

Thanks again, Alex.
The first,third,fourth and sixth, only work if u call the first term n=0 so try replacing n with n+1 so you will get the first term by putting in n=1.
0
quote
reply
damaster275
Badges: 1
Rep:
?
#9
Report 13 years ago
#9
(Original post by alexsmithson)
So would they be:

.
1] . . Formula = ½((n-1)²+21(n-1)+28)


.
3] . . Formula = ½((n-1)²+19(n-1)+14)


.
4] . . Formula = ½((n-1)²+23(n-1)+34)


.
6] . . Formula = ½((n-1)²+7(n-1)+4)

?????
yeah now try to see if u can simplify that...
0
quote
reply
Libertine
Badges: 1
Rep:
?
#10
Report 13 years ago
#10
.
1] . . Formula = ½((n-1)²+21(n-1)+28)
So, ½(n²-2n+1+21n-21+28)
=½(n²+19n+8)

.
3] . . Formula = ½((n-1)²+19(n-1)+14)
So, ½(n²-2n+1+19n-19+14)
=½(n²+17n-4)

Can't be bothered to do the rest, it's all simple stuff.
0
quote
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Fri, 14 Dec '18
  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19

Were you ever put in isolation at school?

Yes (77)
26.92%
No (209)
73.08%

Watched Threads

View All