Number Machine

I have a “number machine” that always affects in the same way whatever number I put in it. For example, when I put in 1, the machine gives me 6; when I put in 3, it gives me 10; when I put in 6, it gives me 16; and when I put in 9, it gives me 22. What will the machine give me if I put in 100?

Extension:
My “number machine” gave me 42. What number did I put in my machine?

I purchased a new “number machine.” This one gives me 1 when I put in 1;3 when I put in 2; 6 when I put in 3; 10 when I put in 4; and 15 when I put in 5. What number will I get when I put in 10? 20? 1000?

(Source: Mathematics Teaching in the Middle School, Nov-Dec 1994)