In a geometric series, each term is generated from the previous term by multiplying by the same number.

For example,

1,  5,  25,  125,  625, .  .  .

Each term is generated from the previous term by multiplying by 5.  These are the powers of 5.

In an arithmetic series, each term is generated from the previous term by adding (or subtracting) the same number.

For example,

1,  5,  9,  13,  17, .  .  .

Each term is generated from the previous term by adding 4.