I see two things in the picture that you could provide more details on:
- the small white spots on the dying frond look like an armoured scale or possibly mealybug
- the dying area (necrotic in plant talk) which consists of a dead brown circular area surrounded by a newer yellowing area. This looks like virus/fungus/bacteria from over watering
Inspect the palm fronds top and bottom for insects. Likely candidates are the white, hard spots seen already which could be armoured scale or small white grains of salt on the underside of the fronds which is spider mites. Both are easily controlled with 5 ml dish soap to 1 litre water. Get a clean rag and wipe the underside of the leaves. Do this three times at five to six day intervals if you find insects. You may wish to rinse the plant fronds after with clean water to get rid of any soap solution.
The most likely problem your plant has is too much water and not enough light. This stresses the plant by making the root medium soggy and low on oxygen. Opportunistic virus/fungus/bacteria get a start in the roots and then move upstairs, so to speak, to the leaves. Most plants can outgrow these problems by changing conditions in the root ball.
Here are my suggestions:
- move to higher light conditions, not hot direct sun but more indirect light closer to a window
- do not fertilize in low light levels. It just raises the level of soluble salts in the soil and the plant cannot use it in low light levels. Most new plants do not need fertilizer for at least the first year and then at lower levels to match the amount of light.
- water when the plant needs water, not on a schedule. Stick your finger in the medium and wait until the top inch of the soil is dry before watering.
- ensure that there is adequate drainage from the bottom of the pot. If water cannot get out it can cause root rot
- test for insects and use soap and water if you find any