SEQUENCE: A succession of numbers formed and arranged in a definite order according to a certain definite rule is called sequence.

The number occuring at the nth place of sequence is called its nth term or the general term, to be denoted by $t_n$

SERIES: By adding the terms of a sequence, we obtain a series.

A series is finite or infinite according as the number of terms added is finite or infinite

https://en.wikipedia.org/wiki/Arithmetic_progression

PROGRESSION: Sequence following certain patterns are called progressions. we will discuss about two types of progressions, namely arithmetical and geometrical.

ARITHMETICAL PROGRESSION(A.P.): it is a sequence in which each term , except the first one, differs from its preceding term by a constant, called the common difference.

in an A.P. we usually denote the first term by a, common difference by d and the nth term by $t_n$. clearly, d=($t_n–t_{n–1}$).