Sum of the Numbers Trick

The video below is only first (Part-1) of the 12 videos. It captures the process that students go through while solving the following problem:

PROBLEM:  The number trick was performed before them a day before.. They were supposed to work out the reason at home... While Poonam starts sharing her views (video- part-1), Shreya claims that she has figured out something and takes over...   

TRICK: I claim that I can predict the sum of 5 numbers without knowing all the numbers, and hence I write this sum on a piece of paper.. I then write the first number on the board... Students tell me the 2nd number. I write the 3rd number. Students tell me the 4th number. I write the 5th number. And very smartly and Instantly, I also write the sum of these numbers as written on that piece of paper....Students take time to add up all these numbers and after 2 minutes get shocked as to how I could predict this sum before-hand.... I do this trick twice... i.e. with two sets of numbers... You can see these problems unerased on the white board....One has the sum 22466 and other has the answer 22541

To check all the twelve videos of this problem, click on this link:
https://www.youtube.com/playlist?list=PLZBBZFls_2nGBmbOh-0HmU5qVSNxu18Ym

Thank You...