KS3 SATS problem - finding the nth term of a sequence

Melanie · 2006-02-25 21:52:07

Hello,
I'm 14 years old and am taking my KS3 moc maths SATs on Monday so as I've been on holiday all this week i've been revising. I was revising how to find the nth term of a sequence and I found it very hard to memorise the method that my teachers taught me to do at school. I have a revision guide from CGP Books and in it suggested that I learnt this formula:
a+(n-1)d+0.5(n-1)(n-2)C

a=The first term in the sequence
d=The difference between the first and second terms in a sequence
c=The change between one difference and the next.

I found that this was a much easier way to work it out, and after doing all the practise questions on the revision guide I searched on the internet to find a couple more questions for me to practise with. Whilst I was looking I came across this webpage: http://www.bbc.co.uk/schools/ks3bitesize/s...ths/46144.shtml

Which suggests that the formula doesn't always work for all number sequences. I don't understand the reply that the SOS teacher wrote and also why would CGP Books teach you a formula that doesn't work every time? So does this formula work or not? Or does the formula only not work for a particular sequence (e.g. triangle numbers or x3 for example).

I'd really appreciate it if I can have some replys by Monday (tommorow) because that's when my test is!

Thank you,
Melanie:D

Jai Ganesh · 2006-02-25 22:56:58

Here's a link that might be of some help. Go here.

Let's try the formula for the different sequences given.

Sequence # 1 :- 1, 3, 6, 10, 15
The formula is a + (n-1)d + 1/2[(n-1)(n-2)C] where a = first term, d = first difference and C = change between one difference and the next.
Here a=1, d=2, C=1. For the 6th term, n=6, given by
1 + (5)2 + 1/2[(5)(4)1] =1 + 10 + 10 = 21.
The sixth term is 21

Sequence # 2 :- 2, 8, 18, 32
Here a=2, d=4, C=4.
For the 5th term, n=5, given by
2 + 4(4) + 1/2 [(4)(3)4] = 2 + 16 + 24 = 42.
But the forumla has given a wrong fifth terms, since the correct fifth term is 50!
Therefore, the explanation given tells that if the first difference is not the same, but the second difference is (as in the above case), there must be a term involving n² for the nth term. By trial and improvement, it can be seen that the nth term is 2n².

Even in the example given earlier, the nth term is (n²+n)/2. Therefore, this formula gives the sixth terms as (6²+6)/2 = 21, which is the correct sixth term.

As it is seen from the examples, the formula a + (n-1)d + 1/2[(n-1)(n-2)C] works in some cases and does not in some others.

Tina13 · 2008-04-28 03:40:39

hi i am Tina
i'm really bored please reply!!!

Tina13 · 2008-04-28 03:58:37

:)hi:) i'm haveing a test comeing up so i'm in a panic
(some reviesing)

Dividing fractions

To divide any number by a fraction:

Multiply the number by the reciprocal of the fraction.
Simplify the resulting fraction if possible.
Check your answer: Multiply the result you got by the divisor and be sure it equals the original dividend.

You can only divide by non-zero fractions.

:)wait i need to get more ideas:)

Tina13 · 2008-04-28 04:45:45

:)hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Dividing mixed numbers

Change each mixed number to an improper fraction.
Multiply by the reciprocal of the divisor, simplifying if possible.
Put answer in lowest terms.
Check to be sure the answer makes sense.

:)ok i'm tierd i'll be back on 2marow at about 6:00pm anyways bye

byeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

TINA13

tina!£

michael.wicks · 2008-06-12 01:11:28

hello this is a reply to melanie: [[a+(n-1)d+0.5(n-1)(n-2)C]
the formula doesn't always work for all number sequences. I don't understand the reply that the SOS teacher wrote and also why would CGP Books teach you a formula that doesn't work every time? So does this formula work or not? Or does the formula only not work for a particular sequence]]

. . .I know its two years late however for anyone else; this formula is only for changing differences e.g 2,5,9,14 you can observe that the difference increases by +1 each time. there is another formula [dn(a-d)] which is for a common difference; meaning a constant difference change between each term. that's why the SOS teacher wrote that the formula [a+(n-1)d+0.5(n-1)(n-2)C] doesn't al;ways work because it all depends on the circumstance. being a changin difference between terms it's guaranteed to work, however, if the difference is the same throughout between each term then you need to use this formula [dn(a-d)] which is also guranteed to work as long as the difference between terms are equal.
In the futre make sure you apply the correct formula for the situation to make sure you get the correct answer. see if the difference changes and if so use the long formula, if not use the short formula, memorising the formulae is not easy at first but as time goes on you will just recall them from memory given you've practised a little. Michael.Wicks 17 kent

Leah (Guest) · 2008-08-27 21:26:45

I would just like to point out that 'Ganesh - Moderator' said in his workings (his reply to Melanie) that the method didn't always work, but he didn't actually do the sum right.

a+(n-1)d+0.5[(n-1)(n-2)C]

So that's the formula, right?

a= first number of sequence
d= difference between the first and second term
C= difference between the value of d and the difference between term two and three

In the example '2, 8, 18, 32...' it should be:
a= 2
d= 6 (difference between 2 and 8 is 6, NOT 4)
C= 4 (difference between 8 and 18 is 10. 10 - 6 = 4)

So if we wanted to work out the fifth term (n = 5) it should look like this:
2+(5-1)6+0.5[(5-1)(5-2)4]
2+(4)6+0.5[(4)(3)4]
2+24+0.5(12x4)
2+24+0.5(48)
2+24+24 = 50!!!

This method does work.

Hehehe

sabah · 2008-09-03 06:48:45

Hi what year are you in? My name is sabah ali I am 11 years old and have just started high school I am in year 7 and i go to Hyde Technology High School. What school do you go to?::D

krassi_holmz · 2008-09-03 12:06:30

OK, here's the whole thruth.
Take the the sums of squares. The sequence starts like this:
0,1,5,14,30...
And we want to determine how is this sequence generated. There's a method, maybe it's called the difference method, which may help us, but ONLY if the generator of the sequence is a polynomial.

We put the numbers in rows like this:

0 1 5 14  30
 1 4 9  16
  3 5 7
   2 2

where under two numbers is their difference. If the generator is polinomial, this process will eventually lead us to a row in which all the numbers are the same (or, which is the same, to a row in which all the numbers are 0)

Call the furst number on the first row

, the first number on the second - , and so on till the first number of the nth row - . Then we use these coefficients in the "magic" formula:

We just have to keep in mind that the sequence is starting at index null, so the first term in our sequence corresopnds to .

In the case of sums of squares, we get:

, which is the wanted formula.

kelc · 2009-03-30 22:50:42

hello im kelc im reali math at maths i mean realii cra[ it realii anoyin though because ut want 2 please ma parents but i no im goin 2 do bad whats a good site that hepls you oh and im in yr9 by thw way
xx

Mevi · 2009-09-22 05:43:59

Tina13 wrote:

hi i am Tina
i'm really bored please reply!!!

Hiya am bored 2

Mevi · 2009-09-22 05:45:53

kelc wrote:

hello im kelc im reali math at maths i mean realii cra[ it realii anoyin though because ut want 2 please ma parents but i no im goin 2 do bad whats a good site that hepls you oh and im in yr9 by thw way
xx

Iya am in yr 9 2 but av u tried mymaths.com i think or mymath.co.uk i think u av 2 sign in tho but itz realliii gd:)

elysha · 2009-11-12 05:36:05

hey i'm elysha and i'm in year 7 and i've got maths homework. it is to find the 5th and 50th number in a squence using the nth term but i don't know how to use the nth term and how to calculate it. my homework has to be in on monday (today is thursday) so please reply within the time please please please i'm desperate lol!

Sarah Rebekah · 2009-11-12 05:59:47

Hi Elysha Welcome to the forum.

bobbym · 2009-11-12 09:14:17

Hi elysha;

Welcome to the forum. Why didn't you post the problem?

umi · 2010-01-07 02:39:27

Mevi wrote:

kelc wrote:
hello im kelc im reali math at maths i mean realii cra[ it realii anoyin though because ut want 2 please ma parents but i no im goin 2 do bad whats a good site that hepls you oh and im in yr9 by thw way
xx
Iya am in yr 9 2 but av u tried mymaths.com i think or mymath.co.uk i think u av 2 sign in tho but itz realliii gd:)

Hi, mymaths.co.uk in a really goog website.
you don't have to login to do it though.
I am in yr7.

LittleMissUSA · 2010-06-05 23:17:43

Hey, I'm tasha leigh. I am filthy rich, spoilt and 16 living in malibu, california. And I hate maths. I find it really difficult, you don' t know what will be in the exams. I am taking my finals this June, I am dreading every waking moment, that means revising non stop. I find it hard to revise solid, I end up talking to my friends on Webcam or Facebook. My dad has load sof mansions back in the USA, but I'm in England. Rain.Rain.Miserable People.Depression or stay home Shopping.Clubbing.Friends and hot. I go a B in my mock exam, but my tutor writes the exams, and he thinks i should be gettting A* if not A. Reading through a KS3 CGP book, the curriculm in America is totally different. Nth term = dn + ( a - d ) (baby are you down,down,down,down,downnnnnnn lol)

bobbym · 2010-06-05 23:33:23

Hi LittleMissUSA. Tasha;

What a great post, easily post of the week!

And I hate maths.

Me too! It's awful. Math is a four letter word and will soon be outlawed. Exam, too.

but I'm in England.

So you live in Malibu and England, at the same time. How do you handle the jet lag? I like Malibu better too. Cameron Diaz surfs there.

Rain.Rain.Miserable People.

Rain is a little depressing but why do they have to speak a foreign language there?

I go a B in my mock exam, but my tutor writes the exams, and he thinks i should be gettting A* if not A.

Okay, you got me here, you hate math, you won't study, your surfing at malibu and your still getting a B! He thinks you can get an A! Well how about really getting an A. Sounds like you are living a great life, mansions, beaches, clubbing, shopping, plenty of dough. You are living the American dream.

Welcome to the forum!

abdulazeez · 2011-07-27 01:47:49

mathematics is easy. all what it takes is focus and intrest. it is what you consider difficult that will be difficult for you. vice-versa:cool:

bobbym · 2011-07-27 01:56:19

mathematics is easy. all what it takes is focus and intrest.

I said the same thing 200 years ago. Look what it did to me ( see the picture on the left ).
If it is easy how about coming on down here and spreading the wealth. I have a few problems for ya!

Welcome to the forum!

Math Is Fun Forum

#1 2006-02-25 21:52:07

KS3 SATS problem - finding the nth term of a sequence

#2 2006-02-25 22:56:58

Re: KS3 SATS problem - finding the nth term of a sequence

#3 2008-04-28 03:40:39

Re: KS3 SATS problem - finding the nth term of a sequence

#4 2008-04-28 03:58:37

Re: KS3 SATS problem - finding the nth term of a sequence

#5 2008-04-28 04:45:45

Re: KS3 SATS problem - finding the nth term of a sequence

#6 2008-06-12 01:11:28

Re: KS3 SATS problem - finding the nth term of a sequence

#7 2008-08-27 21:26:45

Re: KS3 SATS problem - finding the nth term of a sequence

#8 2008-09-03 06:48:45

Re: KS3 SATS problem - finding the nth term of a sequence

#9 2008-09-03 12:06:30

Re: KS3 SATS problem - finding the nth term of a sequence

#10 2009-03-30 22:50:42

Re: KS3 SATS problem - finding the nth term of a sequence

#11 2009-09-22 05:43:59

Re: KS3 SATS problem - finding the nth term of a sequence

#12 2009-09-22 05:45:53

Re: KS3 SATS problem - finding the nth term of a sequence

#13 2009-11-12 05:36:05

Re: KS3 SATS problem - finding the nth term of a sequence

#14 2009-11-12 05:59:47

Re: KS3 SATS problem - finding the nth term of a sequence

#15 2009-11-12 09:14:17

Re: KS3 SATS problem - finding the nth term of a sequence

#16 2010-01-07 02:39:27

Re: KS3 SATS problem - finding the nth term of a sequence

#17 2010-06-05 23:17:43

Re: KS3 SATS problem - finding the nth term of a sequence

#18 2010-06-05 23:33:23

Re: KS3 SATS problem - finding the nth term of a sequence

#19 2011-07-27 01:47:49

Re: KS3 SATS problem - finding the nth term of a sequence

#20 2011-07-27 01:56:19

Re: KS3 SATS problem - finding the nth term of a sequence

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