Ahhhh...someone please help URGENTLY! captain black???? or someone??? PLEASE! im soooo confused?!?!?!?!?!?!?!
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
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
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:
.
Another method: The second differences of your sequenceso 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
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