need help with 16 and 21 step by step Practice Exercises In

need help with #16 and # 21 step by step.

Practice Exercises In Exercises 1-12, write the first four terms of each sequence whose general erm is given. 8. am (-1) 1(n 4) an (-1) (n 3) 10. a n 5 ii. an 20-1 12, a The sequences in Exercises 13-18 are defined using recursion formulas Write the first four terms of each sequence 13. 7 and a am-1 5 for n z 2 14. a1 12 and a an-1 4 for n a 2 15, a 3 and a 4an-1 for n 2 16, a 2 and a San-1 for n ze 2 17. a1- 4 and a 2an-1 3 for n 2 2 18. a 5 and a 3an -1 1 for n 2 2 In Exercises 19-22, the general term ofa sequence is given and involves a factorial. Write the first four terms of each sequence (n 1)! 19, a n! 20, a 21. an 2(n 1) 22, a 2(n In Exercises 2-28 evaluate each factorial expression 18 15 16 20 2114! 2!18! (n 2)! (2n 1)! 31. 33. 39. 5 41. In Ex Use 43. 46. 47.

Solution

16) a1 = 2 ; an = 5an-1

First four terms : plug n= 2, 3, 4

a1 = 2; a2 = 5*a1 = 5*2 = 10 ; a3 = 5a2 = 5*10 = 50

21) an = 2(n+1)!

plug n = 1, 2, 3,4

a1 = 2(2!) ; a2 = 2(3!)

a3 = 2(4!) ; a4 = 2(5!)