Yes, you can install a 1x PCIe card into a 16x or 4x PCIe slot

You have a couple options available to you 1) First is simply looking at the motherboard, many times printed on the PCB near the PCIE slot

In this video, I talk about the different types of PCIe slots and what their uses are There are

pcie gpu slot SATA card for PCIe x1 slot with 8 ports Bizarro

pcie slot for gpu 1 additional PCI-Express x1 slot is needed