Turn on thread page Beta
    • Thread Starter
    Offline

    1
    ReputationRep:
    how do you work out the nth term for a sequence where the diference in numbers is different? for example

    1-st row: 1, 4, 10, 20, 35, 56, 84, ...
    2-nd row: 3, 6, 10, 15, 21, 28, ...
    3-rd row: 3, 4, 5, 6, 7, ...
    4-th row: 1, 1, 1, 1, ...

    after this what do you do next to find the nth term?
    Offline

    2
    ReputationRep:
    changing n'th term is no longer on the gcse sylabus took off from 2002?

    rgrds
    Offline

    1
    ReputationRep:
    Umm, I THINK...that if the first difference is different and you've to move to a second difference it's n^2...

    to find the nth term then I *think* you write the square numbers (1, 4, 9, 16) above the sequence numbers and whatever you do to get from the square numbers to the number in the sequence is the second part ie n2 - 3 if you had to subtract 3 to get the number....but to be honest I always get muddled up so this could be wrong...please someone correct me :p:
    Offline

    0
    ReputationRep:
    use the formula: a+(n-1)+1/2(n-1)(n-2)c
    Offline

    15
    ReputationRep:
    I do know the method, but it is awfully complex if you want the answer straight away - Here goes nothing...

    Ok - you have:

    Term (n): 1 2 3 4 5 6 7....
    Sequence: 1, 4, 10, 20, 35, 56, 84, ...
    1st row: 3, 6, 10, 15, 21, 28, ...
    2nd row: 3, 4, 5, 6, 7, ...
    3rd row: 1, 1, 1, 1, ...

    Now, because we get constant differences in row 3, it will be a cubic equation, and so we will get something in the form an³ + bn² + cn + d.

    As a result, we can write everything algebraically.

    Where n = 1, the equation for the corresponding term will be:
    a + b + c + d

    Where n = 2, the equation for the corresponding term will be:

    8a + 4b + 2c + d

    Where n = 3, the equation for the corresponding term will be:

    27a + 9b + 3c + d

    Where n = 4, the equation for the corresponding term will be:

    64a + 16b + 4c + d (and I'm sure you can see the pattern).

    If we take the differences of these, you'll get the algebraic equivalent of the 1st row sequence (as above).

    As a result, you'll get the seqeunce:

    (7a + 3b + c), (19a + 5b + c), (37a + 7b + c) .... etc.

    Now, if we take the differences of these (as you did with the numbers), we get the algebraic equivalent of the 2nd row sequence (as above).

    As a result, we get:

    (12a + 2b), (18a + 2b)

    Now.... If we take the differences of these, we'll finally get the 3rd row sequence, where all values are the same!

    So, if we take the difference of these, we get....

    6a.... (and it would continue to do so...)

    If 6a = 1, therefore a= 1/6.

    Now if we continue to substitute (going up from the bottom), we find that b= 1/2

    We'll find that c = 1/3, and that d = 0 ( I think...)

    Lets have a check...

    (8*1/6) + (4*0.5) + (2* 1/3) = 4

    Which it does - HURRAH!

    As a result, using the first formula i gave you, you can subsititute in the nth term (the one you want to find) with a being 1/6, b being 0.5 and c being 1/3 (i.e. 1/6n³ + 0.5n² + 1/3n = nth term)

    Phew - that took a long time (any rep for my hard work?? :p:!)
    Offline

    2
    ReputationRep:
    Formula for nth Term, whereby the differences change:

    a+(n-1)d + 1/2(n-1)(n-2)C

    Simple as.

    a = The first term
    d = The difference between the first two terms (ie. the first difference)
    C = the change in the differences (ie. plus two, or minus 3).
 
 
 
Turn on thread page Beta
Updated: June 15, 2005
The home of Results and Clearing

2,343

people online now

1,567,000

students helped last year

University open days

  1. Keele University
    General Open Day Undergraduate
    Sun, 19 Aug '18
  2. University of Melbourne
    Open Day Undergraduate
    Sun, 19 Aug '18
  3. Sheffield Hallam University
    City Campus Undergraduate
    Tue, 21 Aug '18
Poll
A-level students - how do you feel about your results?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.