In "tu sei americano", "AMERICANO" is an ADJECTIVE, and in Italian adjectives agree with the nouns (or the pronouns) they refer to.
So, if "TU" refers to a woman, the adjective that refers to the pronoun "TU" must be SINGULAR FEMININE, so you have "tu sei americana".
Please note that in Italian ADJECTIVES don't begin with a capital letter, even though they refer to a nationality. Of course, if the sentence had been "tu sei un'Americana", in that case "Americana" would have been a NOUN, and you should have written it with a capital letter.
There are some ADJECTIVES in Italian which are invariable (or indeclinable, that is they don't agree, they don't change), but there are not many of them. Some examples are some adjectives referred to colors, like VIOLA, ROSA, AMARANTO, ecc. or the adjective ARROSTO: you say POLLI ARROSTO, QUAGLIE ARROSTO, ecc.
Adverbs used as adjectives and adjectives used as adverbs are invariable as well.