Class 11 Maths Chapter 6 Notes

• Definition of geometric mean
• Definition harmonic progression
• Definition of geometric progression
• Our comprehensive Class 11 Maths Chapter 6 Notes will ensure you're fully prepared for your exams.
• Sequences also called Progressions, are used to represent ordered lists of numbers. As the members of a sequence are in a deinite order, so a correspondence can be established by matching them one by one with the numbers 1, 2, 3, 4,..... For example, if the sequence is 1, 4, 7, 10, ...., nth member, then such a correspondence can be set up as shown in the diagram below:
• Thus a sequence is a function whose domain is a subset of the set of natural numbers. A sequence is a special type of a function from a subset of N to R or C. Sometimes, the domain of a sequence is taken to be a subset of the set {0, 1, 2, 3,...}, i.e., the set of non-negative integers. If all members of a sequence are real numbers, then it is called a real sequence. Sequences are usually named with letters a, b, c etc., and n is used instead of x as a variable. If a natural number n belongs to the domain of a sequence a, the corresponding element in its range is denoted by an. For convenience, a special notation an is adopted for a(n)and the symbol {an} or a1, a2, a3,....,an,...is used to represent the sequence a. The elements in the range of the sequence {an} are called its terms; that is, a1 is the irst term, a2 the second term and an the nth term or the general term. For example, the terms of the sequence {n + (-1)n} can be written by assigning to n, the values 1, 2, 3 ,... If we denote the sequence by {bn}, then If the domain of a sequence is a inite set, then the sequence is called a inite sequence otherwise, an ininite sequence.
• Types of sequences: If we are able to ind a pattern from the given initial terms of a sequence, then we can deduce a rule or formula for the terms of the sequence: we can ind any term of the given sequence giving corresponding value to n in the nth / general term an of a sequence.
• Arithmetic Progression (A.P): A sequence {an} is an Arithmetic Sequence or Arithmetic progression (A.P), if an- an-1 is the same number for all n U N and n > 1. The diference an - an-1 (n > 1) i.e., the diference of two consecutive terms of an A.P., is called the common diference and is usually denoted by d.
• Find the general term and the eleventh term of the A.P. whose irst term and the common diference are 2 and -3 respectively. Also write its irst four terms. If an-3 = 2n - 5, ind the nth term of the sequence. 
• 3. If the 5th term of an A.P. is 16 and the 20th term is 46, what is its 12th term?
• 4. Find the 13th term of the sequence x, 1, 2 - x, 3 - 2x,...
• 5. Find the 18th term of the A.P. if its 6th term is 19 and the 9th term is 31.
• 6. Which term of the A.P. 5, 2, -1,... is -85?
• 7. Which term of the A.P. -2, 4, 10,...is 148?
• 8. How many terms are there in the A.P. in which a1=11 , an = 68, d = 3?
• 9. If the nth term of the A.P. is 3n - 1 , ind the A.P.
• 10. Determine whether (i) -19, (ii) 2 are the terms of the A.P. 17, 13, 9, ... or not.
• 11. If l, m, n are the pth, qth and rth terms of an A.P., show that