(a) Compute the sum 1012−972+932−892+⋯+52−12. (b) Compute the sum (a+(2n+1)d)2−(a+(2n)d)2+(a+(2n−1)d)2−(a+(2n−2)d)2+⋯+(a+d)2−a2.
(a) 101^2 - 97^2 + 93^2 - 89^2 + ... + 5^2 - 1^2 = 101 + 97 + 93 + 89 + ... + 5 + 1 = 1326.
(b) (a + (2n + 1)d)^2 - (a + (2n)d)^2 + ... + (a + d)^2 - a^2 = (a + (2n + 1) d + (a + 2nd + ... + a + d) + a = n(3a + (n + 2)d).
a - sum_(n=1)^26 (-1)^(n + 1) (105 - 4 n)^2 = 5304
b - See detailed step by step answer by "heureka" in the middle of page 531 here: https://web2.0calc.com/members/heureka/?answerpage=531
+109 
