Symmetric continued fraction

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Let (a_i)_{1<=i<=n} be a sequence of positive integers and c be a positive integer such that c divides a_1. Suppose that we have this symmetric of continued fraction [a_n, a_n-1,...,a_1]=c^{-1}[a_1, a_2, ...., a_n]. Can we assume that n is even and a_{n-k}=c^(-1)^{k+1}a_{k+1}, for 0<=k<=n-1?