Learn English – Should I choose “increasingly” or “increasing”

Increasingly is a adverb , increasing is adjective.

Adverbs modify verbs or other modifiers.

Adjectives modify nouns.

So you have to figure out what increasing[ly] is modifying.

An increasingly/increasing large number of people are using online travel sites rather than travel agents.

Large is a modifier that is modifying people - and we are saying that it's getting larger and larger over time. The largeness is increasing.

So increasingly - the adverb is used.