How to find the sum, without adding?

Question

(1)(2+4+6+8+10)
(2)(1+3+5+7+9+11+13)
(3)(2+4+6+8+10+12+14+16+18+20)

Answer 1

The sum cannot be found without some kind of addition somewhere, but ....

look at the last one:
add the first and last ---> 22
add the 2nd and 2nd last ---> 22
add the 3rd and 3rd last ----> 22
how such pairs of 22 can you find?

If you have an odd number of terms, do the same thing, but then don't forget to add the left over middle number,
e.g. for the 2nd
1+13 = 14
3+11 = 14
5+9 = 14
So I have three 14's plus the guy in the middle
sum = 3(14) + 7 = 49

do the first one in the same way.

There is another neat way to add the sum of odd numbers
note the sum of the first two = 1+3 = 4 = 2^2
sum of the first three = 1+3+5 = 9 = 3^2
sum of the first four = ... = 4^2
so...
sum of your first 7 odd numbers = 7^2 = 49 , just as above

Ain't math a lot of fun ??

Answer 2

Sol.(1)There are 5 even numbers
5^2+5=30
Sol.(2)There are 7 odd numbers
7^2=49
Sol.(3)There are 10 odd numbers
10^2+10=100+10=110