A boy is dividing M&Ms between himself and his sister. He gives 2 to his sister and takes 2 for himself. He gives 2 to his sister and takes 4 for himself. He gives 2 to his sister and takes 6 for himself, and so on.

Question

(b) After n rounds, how many M&Ms does his sister have and how many does the boy have?

His sister has 2n

The boy has ? (2n+2n^2) confused on how to calculate his portion

Answer 1

sister has 2 n yes

boy has arithmetic sequence

a1 = 2
d = 2
an = a1 + (n-1) d = 2 + (n-1)2
or an = 2n

sum from n = 1 to n = n
S = (n/2)(a1+an) = (n/2 )(2 + 2n)
S = n + n^2
you got twice as many somehow

Answer 2

Sister 6
Brother 12