Question

1=0
2=1
3=3
4=6
5=10
6=15
I can't figure out a formula

Answer 1

If it is every other justice, why is the 6th justice shaking hands with 15 other people (making him/her the 16th person)?

Answer 2

If there are n justices, and you went to shake hands with everyone but yourself, you shake hands with n-1 justices.

Answer 3

do you see the pattern ?

Answer 4

would it look more like this? @SolomonZelman

Answer 5

No

Answer 6

your second term is 1, not zero.
And the pattern is
\(\LARGE\color{black}{ \bf 0 }\)\(\LARGE\color{red}{ \bf +1 }\)\(\LARGE\color{black}{ \bf =1 }\)
\(\LARGE\color{black}{ \bf 1 }\)\(\LARGE\color{red}{ \bf +2 }\)\(\LARGE\color{black}{ \bf =3 }\)
\(\LARGE\color{black}{ \bf 3 }\)\(\LARGE\color{red}{ \bf +3 }\)\(\LARGE\color{black}{ \bf =6 }\)
\(\LARGE\color{black}{ \bf 6 }\)\(\LARGE\color{red}{ \bf +4 }\)\(\LARGE\color{black}{ \bf =10 }\)
\(\LARGE\color{black}{ \bf 10 }\)\(\LARGE\color{red}{ \bf +5 }\)\(\LARGE\color{black}{ \bf =15 }\)

Answer 7

So you would basically add the # of hand shakes from the previous group to the # of people in the next. But what about 100 and 30 is there an easier way to get the answer than I'm seeing?

Answer 8

@SolomonZelman

Answer 9

yes, this addings are like a sequence

\(\LARGE\color{black}{ \bf 1,2,3,4,5 }\) etc.,

\(\LARGE\color{red}{ \bf a_n=a_1+d(n-1) }\) I hope you are familiar with this red bad boy.

Answer 10

Do you mean

how to get what to add to get 100th term? OR
how to get the 100th term itself?

Answer 11

what do you have to add to get the 100th and 30th term.

Answer 12

use the red formula I posted above. Any questions about it ?

Answer 13

I've never used this what to I plug in where? sorry

Answer 14

I don't have time to explain how recursive formulas work right now, I am really sorry. Tag someone else