1. Write the first 6 terms of the sequence defined by S(1) 3,S(2) 5 S(n) (n - 2) -S(n - 1) + (n - 1) S(n - 2), n > 2 2. Find the recurrence relation of the sequence defined by T(1) 1 T(n)-n.7(n-1), n > 1 3. Find the recurrence relation using the characteristic equation for the sequence defined by F(1) 8, F(2) 16 F(n)-6F(n-1)- SF(n - 2),n 2 3 4. State the linear second-order recurrence relation characteristic equation and formulas for a sequence S(n)a S(n 1)+b S(n - 2) 5. Find P(16) of the sequence defined by 6. Find the recurrence relation of the sequence defined by T1) 1 T(n) T(n 1)+ n,n>1 7. Show F(n 3)2Fn1)F(n),n 2 1 where F(n) is nth Fibonacci number by induction. 8. A species population normally doubles each year, but recently suffers extra losses due to disease-1 during the first year, 2 during the second year, 4 during the third year, then 8, and so forth. State the recurrence relation and determine the population at the end of the sixth year given an initial population P(0)-20 9. Given the following sets: P 12,3,5,7), Q (1,3,5,7,9), R (0,2,4,6,8), S 0,3,6,9), and T 1,2,4,8), where the universal set U P UQURUSUT, find the following: b) S c) Qn R f) 89(P)