Can anyone explain the steps to getting these solutions? Thank you!

1. Consider the sequence defined by a; = (-1)i+l (i 1)2 for i > 1. Compute: (a) (2 points) Li-2 Q2i Solution: ax + 26 + ag = -32 52 72 = -83 (b) (3 points) II-2 021 Solution: 24.06.0g = (-32). (-52) (72) = -11025 2. (15 points) Prove or disprove: For all n e Z, if n mod 4 = 3, then 8|n2 1. Solution: True. Let ne Z, and assume n mod 4 = 3. Since n mod 4 = 3, there exists q e Z s.t. n = = 4q+ 3. Now, n2 1 = (4q+ 3)2 1 = 1692 +249 +9 - 1 = 169 +24q+8 = 8(2q2 +39 +1). Let k = 2q2 +39 +1. Note that n2 1 = 8k. k e z by closure of integers under multiplication and addition. Therefore, 8|n2 1