It sounds like either you have a soft scale (or less likely aphids) The scale as it feeds exudes a clear sticky substance that drips to the lower leaves and onto the floor. It is a common problem with soft scale insects.

The scale maybe green and hard to see. Scales are best controlled with horticultural oil.

As far as pests, areca's usually only get spider mites and scale. There are a few disease issues but they do not cause a sticky substance to form.

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The Buglady
Suzanne Wainwright-Evans, www.bugladyconsulting.com
Educating the world... one bug at a time