Hlily,

Browning of leaf tips especially when it starts at the older, mature leaves almost always means fertilizer burn. If you fertilized your plant, it means you have likely overfertilized it.

If this is the case, you need to repot your jasmine in a new fertilizer-free soil. (If you don't do this, the browning of leaf tips will continue to spread until your plant dies or if you are lucky, until after the high fertilizer level in the soil subsides and becomes 'manageable' to the plant.)

If you didn't fertilize the plant at all, the nursery from where you bought it might have done so. You can also check on soil moisture. Browning of leaf tips is also a sign of dehydration brought about by insufficient watering or too much sun exposure. (The browning in this case however, is not limited to the leaf tips only.)

tropical