Math shortcut: Sum of 3 & 5 consecutive whole numbers

My daughter will be attending her 6 Saturdays MTAP sessions beginning on July 16. We paid 300 pesos for that but I am sure the sessions will help her enrich her mathematical abilities. I do understand that most of the kids find Math a bit hard but I always told my daughter that whatever you needed to study just take time, so give it time kids.

One Math topic which I may share to you is how to get the sum of 3 and 5 consecutive whole numbers without having so much computation, the shortcut should I say.

Examples:
* 1 + 2 + 3 = 6 The sum of three consecutive whole numbers is thrice or three times of the second addend. In this case 2 is the second addend so 2 x 3 = 6. If you have 4 + 5 + 6 it will equal to 15 or 5 x 3.
* 1 + 2 + 3 + 4 + 5 = 15 The sum of five consecutive whole numbers is 5 times of the third addend. In this case 3 is the third addend so 3 x 5 = 15. If you have 10 + 11 + 12 + 13 + 14 it will equal to 60 or 12 x 5.

There’s this MTAP question that asked for 5 consecutive whole numbers that equal to a certain number wherein you can apply this concept.

Example: Find 5 consecutive whole numbers that equal to 110. First, you need to divide 110 by 5. Why 5? Because you are looking for 5 consecutive whole numbers. The answer will be 22 and it will serve as the third number or middle addend. To get the 5 numbers, get the 2 numbers before 22 and 2 numbers after 22 and that is the answer (20, 21, 22, 23, 24).