NCERT Class 11 Maths Sequences And Series Questions

By a sequence, we mean an arrangement of numbers in a definite order according to some rule. We denote the terms of a sequence by a1, a2, a3, ... , etc., the subscript denotes the position of the term.

In view of the above a sequence in the set X can be regarded as a mapping or a function f : N→ X defined by

f (n) = t_n ∀ n ∈ N.

Domain of f is a set of natural numbers or some subset of it denoting the position of term. If its range denoting the value of terms is a subset of R real numbers then it is called a real sequence.

A sequence is either finite or infinite depending upon the number of terms in a sequence. We should not expect that its terms will be necessarily given by a specific formula.

However, we expect a theoretical scheme or rule for generating the terms.

Let a₁, a₂, a₃, ... , be the sequence, then, the expression a₁ + a₂ + a₃ + ... is called the series associated with given sequence. The series is finite or infinite according as the given sequence is finite or infinite.

Remark When the series is used, it refers to the indicated sum not to the sum itself. Sequence following certain patterns are more often called progressions. In progressions, we note that each term except the first progresses in a definite manner.

9.1.1 Arithmetic progression (A.P.) is a sequence in which each term except the first is obtained by adding a fixed number (positive or negative) to the preceding term.

Thus any sequence a₁, a₂, a₃ ... a_n, ... is called an arithmetic progression if a_n + 1= a_n + d, n ∈ N, where d is called the common difference of the A.P., usually we denote the first term of an A.P by a and the last term by l
The general term or the nth term of the A.P. is given by
                                                        a_n = a + (n – 1) d
The nth term from the last is given by a_n = l – (n – 1) d

Please refer to attached file for NCERT Class 11 Maths Sequences And Series Questions