Which term applies to numbers that cannot be written in this form a/b

Assuming 'a' and 'b' are integers, with b as nonzero, then a/b is known as a rational number. The term "ratio" is buried in "rational". A ratio is effectively a fraction of two values so that's a good way to remember the term. Some examples of rational numbers are 2/3 or 4/9. Whole numbers are rational because something like 7 is the same as 7/1

Any numbers that cannot be written as a ratio of whole numbers, we consider them irrational (aka opposite of rational, or not rational). Something like pi = 3.14 or sqrt(2) = 1.414 are irrational as we cannot express them in the form a/b. We can get close but not exact. 

In summary, the answer is irrational

, and

for

step-by-step explanation:

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

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

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