Thread: Coursework Help Nth Term!!!

I am confused

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

Ahhhh...someone please help URGENTLY! captain black???? or someone??? PLEASE! im soooo confused?!?!?!?!?!?!?!

There are a number of ways of doing this, which is best depends
upon what you are expected to do/allowed to assume.

Originally Posted by lilblob

I am confused

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:

.

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:

.

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
quadratic in n. So suppose:



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:





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

RonL

Thanks! That helps a lot! You are a genius!

lilblob