but it's just logic for that second of yours ...
as you see first number is changing by the one so it will be n* od k* ... now let's look at the second ... how can u write 2+5+8+11 ? as you see it's next one always bigger from the one before by 3 ... so you know that first is n or k or whatever ... so second is 3k and you now do -1 because of the first first member to get that what you need
because without -1 youl get 1*3 + 2*6 +3*9 and so on ... so it must be k(3k-1)
now go back at first example
so it's .... for just k.... will be 1+2+3+4+... do you see pattern similar to yours ? perhaps ?
k*k = 1*1 +2*2+3*3+4*4+....
you can try like this ... you know that your series change by one ? ok so whatever you have you can write as 1* something + 2* something(the same) + ... and then compare with that what you need and then just solve what is that something that when multiplied with number of the member will give you your sequence ... sorry for bad explaining ... few problems with English