Sum of n consecutive numbers

Is there a shortcut method to working out the sum of n consecutive positive integers?

Firstly, starting at $1 ... 1 + 2 + 3 + 4 + 5 = 15.$

Secondly, starting at any other positive integer ...($10$ e.g.): $10 + 11 + 12 + 13 = 46$.

Answer

Take the average of the first number and the last number, and multiply by the number of numbers.