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Sequence and Series Learning Objectives atthe course of this chapter, you will be able to: Ii-L ently the common difference of an erithme- 11-3. Learn arithmetic,geometric and harmonic tic sequence means Ut-2 Understend the sum of n terms of an arith- mmetico-geometric series sum Sequence | Types of Sequence Forecasts web ees ta ines a cok focobtaining the terms. I I EXAMPLE: it TS. .-.. =, --- 18. a Sequence. 23 x A sequence is a fimetion whose domain is the set Vof natu- raf sexmabers. Since the domuim for every sequence is the set of N natural numbers, therefore 2 sequence is represented by its renge. f: N = RK, then Amb =4. 7 e Nis calleda Real Sequence A sequence whose range is a subset of F is called a reat Séquence. “ EXAMPLES: 125,818 - 2 4,1,2.-5,-- 3. 3,-9, 27, -81.--- On the basis of the number of terms there are two types of sequence. 1. Finite sequence: A sequence is said to be finite if it has finite number of terms. 2. Infinite sequence: A sequence is said to be infinite if it has infinite number of terms. Series By adding or subtracting the terms of a sequence, we getan expression which is called a series, If a,, Ay Ay 4 QS a sequence, then the expression a, +a, tat. - +a, isa series, “EXAMPLES: 14243444047 2. 244484164... Progression Itis not necessary that the terms of a Sequence always fol- low a certain pattem or they are described by some explicit formula of the n® term. Those Sequences whose terms fol- low certain patterns are called progressions. 
