Thanks in advance!

6. (5 points) Prove that for all neZ+ 21 divides 4"+152n-1 7. Consider the following recurrence relation: an + 4an-1-0; a,--12. (a) (2 points) Determine, a2, as, and a4 (b) (6 points) Solve the recurrence relation and verify your answer 8. Consider the following two relations (R, and R2) defined from. A = {2,3,4,5) to B = 2,4,6) where: (m, n) E R1 iff m-n = 1; (m, n) E R2 iff mn (a) (5 points) List the ordered pairs in the relations Ri and R2 (b) (5 points) Determine whether R1 and R2 are: reflexive, symmetric, antisymmetric and transitive