Sequences and Series Class 11

 

Sequences and Series class 11 – The different numbers occurring in any particular sequence are known as its terms. The terms of a sequence are denoted by \(a_{1},a_{2},a_{3},……,a_{n}\). If a sequence has finite number of terms then it’s known as a finite sequence. A sequence is termed as infinite, if it is not having definite number of terms. The nth term of an AP is given by a + (n-1) d. Between any two numbers ‘a’ and ‘b’, n numbers can be inserted such that the resulting sequence is an Arithmetic Progression. \(A_{1},A_{2},A_{3},……,A_{n}\) be n numbers between a and b such that a, \(A_{1},A_{2},A_{3},……,A_{n}\), b is in A.P.

Here, a is the 1st term and b is \(\left ( n+2 \right )^{th}\) term. Therefore,

b = a + d[(n + 2) – 1] = a + d (n + 1).

Hence, common difference (d) = \(\frac{b-a}{n+1}\)

Now, \(A_{1}\;=\;a+d\;=\;a+\frac{b-a}{n+1}\),

\(A_{2}\;=\;a+2d\;=\;a+\frac{2(b-a)}{n+1}\),

\(A_{n}\;=\;a+nd\;=\;a+\frac{n(b-a)}{n+1}\)

The nth term of a geometric progression is given by \(a_{n}\;=\;ar^{n-1}\)<

Sequences and Series class 11 Examples

Sequences and Series Class 11
Sequences and Series Class 11
Sequences and Series Class 11
Sequences and Series Class 11
Sequences and Series Class 11
Sequences and Series Class 11

 


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