# Basic Concepts

• Sequence is an arrangement of numbers in definite order according to some rule
• A sequence is a function whose domain is a set of natural numbers. If the range of a sequence is a subset of real numbers (complex numbers), then it is called a real sequence (complex sequence)
• Finite sequences : A sequence is said to be finite if it has finite number of terms.
• Infinite sequences : A sequence is said to be infinite if it has infinite number of terms.
• If a1 , a2 , a3 - - - an is a sequence, then the expression a1 + a2 + a3 + - - - - - + an is a series.
• Sequences following specific patterns are called progressions.

### Part4: View the Topic in this video From 00:40 To 37:04

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• The finite series x1 + x2 + x3 +..... +xn =\sum_{k=1}^{n} \ x_{k}
• The infinite series x1 + x2 + x3 +..... +xn +...... ∞ = \sum_{i=1}^\infty \ x_{i}