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:

\((a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + \cdots + (a+d)^2 - a^2.\)

Guest Jun 24, 2020

#3**+1 **

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).

gwenspooner85 Jun 24, 2020