In this note , lets denote the nth term of the triangular number sequence as Tn . First lets take the sequence 3,6,15,28,55,78..... . We could observe that these numbers are T2 , T3 , T5, T7, T11,T13 .......... i.e the prime number term . So, the relation that can be seen between the sequences : S1 = 3,6,15,28,55,78 and S2 = 2,3,5,7,11,13 is 3x2 = 6, 5x3=15, 7x4=28 , 11x5=55 , 13x6=78 except the number 2. I hope that you can understand this property
Second, in the sequence 0,1,3,6,10,15,21,28,36,45,55,66..... We could see that 0,1 are divisible by 1. 3,6 are divisible by 3. 10,15 are divisible by 5. 21,28 are divisible by 7. 36,45 are divisible by 9 ............. Hence ,we can understand that if n is an odd term, then nth term and n-1th term would be divisible by n.
Sorry to my followers who would have expected much in this note !!!