There are 7 special subjects at Ichiro's school: art, music, gym, library,
enrichment, typing, and research. Students only take 1 special subject
each school day. A special subject is not taken more than once a week.
Assume that special subjects are assigned randomly.
Ichiro has library on Monday. If the remaining subjects during the school week
are assigned randomly from the other 6 subjects, what is the probability that he
has art on Friday?

The probability is probably something like this:

Monday; Library, Tuesday; research, Wednesday; typing, Thursday; music, Friday; art

However, there are more probabilities to order this but obviously, you can not fit them all and there are 7 special subjects. So, the choice is probably up to you...

1010: 3030

is it i think

, 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