Each level of a smartphone app adds more gems for you to match. on level one, there were 13 gems. on level twelve, there were 123 gems. when you complete all twelve levels, how many total gems will you have matched?

First find the rate or common difference if it exists.

(123-13)/(12-1)

110/11

10  So this essentially form an arithmetic sequence because each term is a constant difference with respect to the previous term.

The sum of an arithmetic sequence, in simplest terms, is the average of the first and last terms times the number of terms, in this case:

(12-1+1)(13+123)/2

12(68)

816

So the player will have matched 816 gems in total for the twelves rounds.