A sequence occurs when a melodic pattern is repeated, starting on different notes each time. Each repetition has the same melodic shape and melodic rhythm as the original statement.

The starting notes may be in an ascending or descending direction, based on notes in the underlying scale, an arpeggio on the underlying harmony, or some other interval. Typically the pattern is played three times.

The last 4 Bar Phrase in Section B of Di Sarli’s Bahia Blanca is a sequence. The same one bar melody is played three times, the second and third time a scale step lower that the preceding one.

A sequence isn’t necessarily in the melody. In this example the piano also plays a sequence in a countermelody-like relationship with the melody. The piano sequence is a bar of four bass notes, three in an ascending then one a step down; repeated from different starting notes.
Sequences in Bahia Blanca
Bahia Blanca, Section B, fourth 4 Bar Phrase, bars 29-32.

An arpeggio is a chord (a harmony) that is broken up into individual notes, that is, the notes are heard one at a time in succession, not simultaneously. Arpeggios are frequently heard in the melody and somewhat less in the accompaniment.

More information, music and audio examples are here.

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