Recall the set of payoffs in a game of chuck-a-luck: a. You win one times your bet if your number appears on one die.
b. You win two times your bet if your number appears on two dice.
c. You win three times your bet if your number appears on three dice
d. You lose your bet if your number appears on none of the dice.

You play 50 consecutive games of chuck-a-luck, betting 5 chips in each of the first 30 games, and 10 chips in each of the remaining 20 games. By the end of these games you'll expect to:

1. lose 19.5 chips
2. lose 34.1 chips
3. lose 27.3 chips
4. win 20.4 chips
5. break even

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

the weight of the object inside the box!

it will take 9 minutes                

i don't even know how to read that, ill try to do it if you translate it into english.