Arithmetic sequence

Arrange the numbers in increasing value: 1/6, 1/3, 1, 2. For a sequence to be arithmetic, the difference of two consecutive terms (any term - preceding term) must be equal. Let us check:

(a) 1/3 - 1/6 = 1/6
(b) 1 - 1/3 = 2/3
(c) 2 - 1 = 1

Since the difference of two adjacent terms are not equal, the given terms do not form into arithmetic sequence.

Arithmetic sequence must be in increasing and deceasing value.

No. The sequence must be 1/3, 1/6, 1, 2.
a, a+d, a+2d, a+3d. Where a = 1/3, and d = 1/3.