# 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 $a_{n}\;=\;ar^{n-1}$<