Question 971762
Your dash sign at the start must be an accidental stray character.  There is a difference pattern showing.


1 to 2, added 1.
2 to 7, added 5.
7 to 14, added7...........


Now the dash must really be intentional.
-1 to 2, added 3.
2 to 7, added 5.
7 to 14, added 7.
14 to 23, added 9.



-1 to 2, added 3._______-1+2+1, n=2
2 to 7, added 5._______-1+(2+1)+(2+3), n=3
7 to 14, added 7.______-1+(2+1)+(2+3)+(2+5), n=4
14 to 23, added 9._____-1+(2+1)+(2+3)+(2+5)+(2+7), n=5


Each term is based on a summation.
You may be able to finish this on your own.  You will need to think carefully about each section shown above.


(2+1+(n-2)2),
(2+(1+(n-2)*2)), represents the last expression added.
Does this work for n=3?  n=5?
Yes for n=3; yes for n=5.


NOTE:  The above shown work is a search for the pattern.  I DID NOT finish answering; I show there the effort of searching for the pattern.  Can YOU finish this?