'A' is an indefinite article used before consonant sounds. 'An' is an indefinite article used before vowel sounds. 'The' is a definite article used before definite/specific things/superlatives etc. 'The' is also used before adjectives which represent the entire class and not a specific person. Here, the adjective 'rich' is used without the noun and the adjective represents the entire class of rich people, not one specific rich person. The adjective is used as a noun in this case.
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