In problems 5 and 6 a sequence is defined recursively. Find an explicit formula for the sequence. 5. a =--ak-1 3 -ak-2, for each integer k 22, a. =3, a, =4 6. ax =2ak_1+5ak_2, for each integer k 22, a, =1, a, = 3 7. Draw the directed graph for the following relation R defined on the set A. A= {1,2, 3, 4} x Ry - y|(x-1) 8. For the following relations defined on the set A= {1,2,3} , determine whether the relation is reflexive, symmetric, and/or transitive. (a) R= { (1, 1), (1, 3), (3, 1), (3, 3) } (b) R= { (1, 1), (1, 2), (2, 2), (3, 3) } 9. Determine whether the relation R on the set of all integers is reflexive, symmetric, and/or transitive, where (m, n) ER if and only if (a) mn21 (b) 71 (m-n)