I’m thinking about this question in the sense that we often have a term (−1)n for an integer n, so that we get a sequence 1,−1,1,−1… but I’m trying to find an expression that only gives every 3rd term as positive, thus it would read;

−1,−1,1,−1,−1,1,−1,−1…Alternatively a sequence yielding 1,1,2,1,1,2,1,1,2… could also work, as n could just be substituted by it in (−1)n

**Answer**

Let F_n be the Fibonacci sequence 0,1,1,2,3,5,8,13,21,34,… then a possible sequence is (-1)^{F_{n+1}}

**Attribution***Source : Link , Question Author : Kristaps John Balodis , Answer Author : Community*