I have three marbles in a bag. One is purple and the other two are green. What is the probability of pulling a green marble out of the bag?

1/3 would be the chances you'd pick purple, because there's only 1 in 3 that's purple out of all 3 marbles.

With green it would be 2/3 because there's twice the number of green marbles than purple.

If there's 1 of purple and 1 of green, the probability would then be 1/2 of picking either colour.

, 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

whew you’re speaking a different language