Hiya
In the number pathern 1.3.6.10.15.21.34
I found the recursive formula an+1-an=n+1
now i need to find a formula for n.
shouldent it be somthing like an+1=n ?
Well spotted. At this thread (which I assume post #1 is following up from) that's the sequence I had in mind too ..... 1,3,6,10,15,21,34 is more difficult and the formula I gave, $\displaystyle a_{n+1} - a_n = n+1$, clearly fails to give $\displaystyle a_7 = 34$ ....
A further clue is needed perhaps ....? Here's a massive one -
1=1x(1+1)/2
3=2x(2+1)/2
6=3x(3+1)/2
10=4x(4+1)/2
etc.....
The rule should come as no surprise since $\displaystyle a_n$ is the sum of the first n positive integers ......
btw 1 (as I suggested in the other thread) you could always look into the general method of solving a recurrence relation of the form $\displaystyle a_{n+1} - a_n = \, \text{polynomial function of } n$.
btw 2 it's been said that mathematics is the study of patterns. And what better way of developing this than questions like this one ......