List the terms of each finite sequence 1 an13 n143 for 1 les

List the terms of each finite sequence. 1 a_n=1/3 (n-1)+4/3 for 1 lessthanorequalto n lessthanorequalto 3 2. b_1 = 5, b_2 = 2, b_n = b_(n-1) + b_(n-2) for 3 lessthanorequalto n lessthanorequalto 6

Solution

1) an = (1/3)(n-1) +4/3 for 1 <=n<=3

a1 = (1/3)(1-1) =0

a2 = (1/3)(2-1) = 1/3

a3 = (1/3)( 3-1) = 2/3

2) b1 = 5 , b2 = 2

bn = bn-1 +bn-2

for 3<=n<=6

b3 = b2 +b1 = 2 +5 =7

b4 = b3 +b2 = 7 +2 = 9

b5 = b4 +b3 = 9 +7 = 16

b6 =b5 +b4 =16 +9 = 25