Question

Difference between arithmetic series and sequence?

Answer 1

Series means the sum of first few terms while sequence means the terms. 
a, a+d, a+2d,.... is an A. S. where you consider individual term(s) 
a+ (a+d) + (a+2d)+,.... is the series.

Answer 2

A sequence is an arrangement of numbers in a definite order according to some rule.
For example, 1, 1, 2, 3, 5, 8,.... is a sequence in which a1= 1
a2=1
a3 = a1+ a2 = 1+1= 2
a4= a2+ a3= 1+2=3
a5= a3+a4= 2+3= 5 ..... and so on.
On the other hand, an Arithmetic Series or Progression(AP) is a sequence in which each term differs from its preceding term by a constant. The constant is called the common difference of the AP. It is denoted by 'd'.
For example, 2,6,10,14,18,...... is an AP in which
a1= 2
a2= 2+4=6
a3= 6+4= 10
a4= 10+4=14
Here the common difference 'd' is 4.
It is being added to each term to get the next term.
Hope it helps!