Photoelectron spectroscopy was applied to characterize electronically excited states of carbon clusters consisting of odd number atoms, C-2n+1(-) (n = 2 - 7). By optimizing the cluster generation condition so that the fraction of C-n(-) anions with a linear form increases, the energy difference between the ground and the first excited states of the carbon linear chains up to C-15(-) was systematically examined. As a result, it was found that the photoelectron second bands are attributed to the first excited triplet states of neutral carbon linear chains. The monotonous decrease of the excitation energy found for C7-15 clearly indicates that these linear chains possess a common electronic property for the lowest triplet states. Furthermore, by analyzing the decrease of the excitation energy in the triplet manifold, it was found that the gap tends to converge to almost zero by increasing a length of carbon chain.