= Given:
N = Natural number
| = Integer
Q = Rational number
Q' = Irrational number
R = Real number

The number
7/22
is in which of the sets N, I, Q, Q', R?

  Q, R

Step-by-step explanation:

All of the listed sets of numbers are Real numbers. The fraction is not an integer, so is not in sets I or N. Because it is a fraction, it is in set Q, and because R includes Q, ...

  the number is in sets Q and R

, 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