Here is a harmonic sequence which comprises a progression of 5ths, each with added 7th chords. It uses a series of suspensions which allow each chord to move smoothly into the next.
The complete progression of 5ths is I-IV-VII-III-VI-II-V-I. Each chord moves to the chord a 5th lower.
The added 7th is a dissonant note, which is prepared and resolved in the normal way. The 7th is the note which forms the suspension.
In chord IV7, the dissonant 7th is E (in the soprano). The E is prepared in the previous chord (I7) and resolves down by step to D in the following chord (vii°7). In chord vii°7, the dissonant 7th is A (in the alto). The A was prepared in IV7 and resolves down to G in iii7. And so on. The preparations, dissonances and resolutions alternate between two parts (the soprano and alto in this case) as an interlinking chain. Notice that there is very little movement within each individual part (apart from the bass).
This type of sequence was particularly common in Baroque times, but can be found in music from any era. The sequence may be used in its entirety, or just a shorter section.
In music with a continuo (figured bass) part, harmonic sequences are fairly easy to spot, because you will see repeated numbers in the figured bass. In this example from Corelli’s Trio Sonata Op.3 no.11 Presto Movement, the row of “7s” in bars 14 and 15 shows the harmonic sequence with suspensions. (This is a realisation of the continuo part).
Notice the pattern of the bass line, which is a series of rising 4ths and falling 5ths. Where there is no figured bass to help you, the shape of the bass line can sometimes be a clue to where there is a sequence.