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, , clearly fails to give ....
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 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 .
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 ......