determine if the squenceces are aritmetic, geometric or nither

Question

a) 2/3, 1, 4/3, 5,2 ,2

b) 8/3, 4/3, 2/3, 1/3, 1/6, 1/12

Answer 1

1st is Neither, unless it was copied incorrectly

first 3 terms suggest an arithmetic sequence with a common difference of 1/3

2/3 + 1/3 = 1

1 +1/3 = 4/3

4/3 + 1/3 = 5/3

5/3 +1/3 = 2

2+1/3 = 2 1/3

2/3,1, 4/3, 5/3, 2, 2 1/3 is an arithmetic sequence

with nth term = an = 1/3 + (n-1)(2/3)

but

2/3,1, 4/3, 5, 2, 2 is not arithmetic or geometric

2nd is Geometric

8/3, 4/3, 2/3, 1/3, 1/6, 1/12

2nd has a common ratio of 1/2. each term is 1/2 the preceding term

nth term is an = (8/3)(1/2)^(n-1),

6th term = (8/3)(1/2)^5 = (8/3)/32 = 1/12