In the wood industry, logs are commonly quality screened by discrete X-ray scans on a moving conveyor belt from a few source positions. Typically, the measurements are obtained in a single two-dimensional (2D) plane (a "slice") by a sequential scanning geometry. The data from each slice alone does not carry sufficient information for a three-dimensional tomographic reconstruction in which biological features of interest in the log are well preserved. In the present work, we propose a learned iterative reconstruction method based on the Learned Primal-Dual neural network, suited for sequential scanning geometries. Our method accumulates information between neighbouring slices, instead of only accounting for single slices during reconstruction. Evaluations were performed by training U-Nets on segmentation of knots (branches), which are crucial features in wood processing. Our quantitative and qualitative evaluations show that with as few as five source positions our method yields reconstructions of logs that are sufficiently accurate to identify biological features like knots (branches), heartwood and sapwood.