An iterative strategy for the stereodivergent synthesis of unbranched 1,5,9,n-polyenes (and -polyynes) was investigated. Starting from a terminal alkyne the iteration cycle consists of a C3 extension (allylation), a chemoselective hydroboration, an alkyne reduction, and an oxidation of the associated alcohol with subsequent C1 homologation. Double bond geometry is controlled using stereoselective alkyne reductions, employing either the Lindlar hydrogenation protocol or an aluminum hydride reduction. In a model sequence it was demonstrated that the strategy is applicable to the synthesis of 1,5,9,n-polyenes with any possible double bond configuration accessible in equally high efficiency and selectivity. It is worth noting that our approach does not require any protecting group chemistry. Furthermore, using the same strategy, the first total synthesis of chatenaytrienin-4, the proposed unsaturated biosynthetic precursor of the bis-THF acetogenin membranacin, was examined. Thus, the all-cis 1,5,9-triene natural product was prepared in 15 steps from commercially available starting materials in 6% overall yield.