X/y tables?

suppose that at the first meeting of the house of represenatives all 435 of them shook hands with every member. how many handshakes took place? 1 person=0shakes.2ppl=1 shake.3ppl=3shakes.4ppl=6shakes.5ppl=10s… 7ppls =21shakes. do you see the pattern? please write the formula and solution. formula( y=gx (squared) +fx+e) please fill in the formula also.