Sequence 1 is a list of the:

nine muses of Greek mythology as follows (bold for missing letters):

Calliope, Clio, Euterpe, Erato, Melpomene, Polyhymnia, Terpsichore, Thalia, Urania

Sequence 2 is the order of the:

British monarchs as follows (bold for missing letters):

Anne, George I, George II, George III, George IV, William IV, Victoria, Edward VII, George V, Edward VIII, George VI, Elizabeth II

Sequence 1 is a list of the:

nine muses of Greek mythology as follows (bold for missing letters):

Calliope, Clio, Euterpe, Erato, Melpomene, Polyhymnia, Terpsichore, Thalia, Urania

Sequence 2 is the order of the:

British monarchs as follows (bold for missing letters):

Anne, George I, George II, George III, George IV, William IV, Victoria, Edward VII, George V, Edward VIII, George VI, Elizabeth II

Sequence 4 is a list of the:

second letters of the abbreviation of US states (bold for missing letters).
The order is alphabetical based on the full state name.

AL, AK, AZ, AR, CA, CO, CT, DE, FL, GA, HI, ID, IL, IN, IA, KS, KY, LA, ME, MD...

Sequence 2 is a list of the:

British monarchs as follows (bold for missing letters):

Anne, George I, George II, George III, George IV, William IV, Victoria, Edward VII, George V, Edward VIII, George VI, Elizabeth II

Sequence 1 is a list of the:

nine muses of Greek mythology as follows (bold for missing letters):

Calliope, Clio, Euterpe, Erato, Melpomene, Polyhymnia, Terpsichore, Thalia, Urania

Sequence 2 is the order of the:

British monarchs as follows (bold for missing letters):

Anne, George I, George II, George III, George IV, William IV, Victoria, Edward VII, George V, Edward VIII, George VI, Elizabeth II