At Caesar's Palace Casino in Vegas, there were three poker players, Alice, Bernie and Craig. At the beginning of the night the amount of money each had was split in the ratio 7 : 6 : 5, with Alice starting with the most and Craig the least. At the end of the night, Alice was still ahead and Craig still last, but the money was divided according to the ratio 6 : 5 : 4. This meant that one of the players was up by $12.

What were the combined assets of the players at the beginning of the evening, in dollars?

what is all that apply?

a

step-by-step explanation:

the answer is a

, 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