please give thorough explanations, i am confused about how to solve this properly... I thought using a^2 - b^2 = (a - b)(a + b) would work, but I don't think it is the most efficient way.
(a) Compute the sum:
\(101^2 - 97^2 + 93^2 - 89^2 + \cdots + 5^2 - 1^2.\)
(b) Compute the sum:
\((a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + \cdots + (a+d)^2 - a^2.\)
This has been posted before. Try searching for it.
Using difference of squares is the most efficient way. I don't know how to do part (b), but I can certainly explain part (a).