# Coursework Help Nth Term!!!

• Nov 13th 2005, 03:49 AM
lilblob
Coursework Help Nth Term!!!
I am confused :confused: :confused: :confused: :confused: :mad:

I am trying to find a formula to link these numbers for a part of my GCSE coursework (i.e nth term) could someone please show me how i can do this??

1 2 3 4 5
3 6 10 15 21....

I know that the numbers underneath are triangle numbers, but i am confused about nth term, and dont know how to work this out.

so far i have done this:

1 2 3 4 5
3 6 10 15 21
3 4 5 6 - Difference
1 1 1 - Difference

But i do not know what these numbers mean? and how you can work out the nth term from it? (does the difference being incosistant then consistant show something? like n+1 or 1n or something? PLEASE HELP!!!)i want to know how i can get the answer! so please show me HOW you can find it!

HELP WOULD BE MUCH APPRECIATED!!!
Thanks
lilblob :)
• Nov 13th 2005, 05:40 AM
lilblob
Captian Black can u help?
• Nov 13th 2005, 08:59 AM
CaptainBlack
There are a number of ways of doing this, which is best depends
upon what you are expected to do/allowed to assume.

Quote:

Originally Posted by lilblob
I am confused :confused: :confused: :confused: :confused: :mad:

I am trying to find a formula to link these numbers for a part of my GCSE coursework (i.e nth term) could someone please show me how i can do this??

1 2 3 4 5
3 6 10 15 21....

I know that the numbers underneath are triangle numbers, but i am confused about nth term, and dont know how to work this out.

You correctly observe that the sequence you are asked to find
the n-th term for is the sequence of triangular numbers, except
it starts from 3 rather than 1.

Presumably you know the formula for the n-th triangular
number:

$\displaystyle T(n)\ =\ n\cdot(n+1)/2$.

Now to get this to start from 3 rather than 1, just replace
n by (n+1) in the formula to give the n-th term of your
sequence:

$\displaystyle S(n)\ =\ (n+1)\cdot(n+2)/2$.

Quote:

so far i have done this:

1 2 3 4 5
3 6 10 15 21
3 4 5 6 - Difference
1 1 1 - Difference

But i do not know what these numbers mean? and how you can work out the nth term from it? (does the difference being incosistant then consistant show something? like n+1 or 1n or something? PLEASE HELP!!!)i want to know how i can get the answer! so please show me HOW you can find it!

HELP WOULD BE MUCH APPRECIATED!!!
Thanks
lilblob :)
Another method: The second differences of your sequence
are constant. This should tell you that the sequence is a

$\displaystyle S(n)\ =\ An^2+Bn+C$

Now we know that S(1) = 3, S(2) = 6, and S(3)=10. So
we have the three simultaneous linear equations for A, B and
C:

$\displaystyle A\ \ \ +\ \ B\ +\ C\ =\ 3$
$\displaystyle 4A\ +\ 2B\ +\ C\ =\ 6$
$\displaystyle 9A\ +\ 3B\ +\ C\ =\ 10$

Solving these for A, B and C will also give you the formula
for the n-th term of your sequence.

RonL
• Nov 13th 2005, 09:40 AM
lilblob
Thanks! :) That helps a lot! You are a genius! :D

lilblob :cool: