What is the formula and answer for the following?

Question

100-98+96-94+92....+12-10+8-6+4-2.

Thanks for the help!

Answer 1

formula=(100+96+92+.........)-(98+94+90+.........)
sum of arithmetic progression=Sn=(1/2)n[2a+(n-1)d]
(1/2)*25{[200+24*2]-[196+24*2]}
(1/2)*25*(248-244)
(1/2)*25*4
=50

Answer 2

Well, each of the pairs (100-98, 96-94, etc) all add up to 2.

There will be 25 of these pairs (100/4), so the sum will be 50.

Not sure about the formula.

Answer 3

Multiples of 4 (4, 8, 12,...) are added, while multiples of 2 and not 4 (2, 6, 10,...) are subtracted.
Think of the set of 50 numbers as 25 pairs of neigboring numbers, and take each one's sum: (-2 + 4), (-6 + 8), (-10 + 12),...
Notice how the sum of each pair is +2, and since there are 25 pairs, the sum of the whole set must be 25*2 = 50 (and it is).