Real life applications of Progression
1. If you put 10 Rs every day on your piggy bank, you want to know the money after some x days
2. If salary of a person is Rs 5000 & it increase by 1000 Rs every year, what will be salary after x years?
3. If salary of a person is Rs 5000 & it doubles every year, what will be salary after x years?
4. The lengths of the rungs of a ladder decrease uniformly by 3 cm from bottom to top. If the bottom rung is 50 cm in length, how to find length of any rung?
The various numbers occurring in a sequence are called its terms. We denote the terms of a sequence by a1, a2, a3, …, an, …, etc., the subscripts denote the position of the term. The nth term is the number at the nth position of the sequence and is denoted by an. The nth term is also called the general term of the sequence.
A sequence containing finite number of terms is called a finite sequence. A sequence is called infinite, if it is not a finite sequence.
Let a1, a2, a3,…, an, be a given sequence. Then, the expression a1 + a2 + a3 +,…+ an +... is called the series associated with the given sequence. The series is finite or infinite according as the given sequence is finite or infinite.
Series are often represented in compact form, called sigma notation, using the Greek letter Σ( sigma) as means of indicating the summation involved. Thus, the series a1 + a2 + a3 +... + an is abbreviated as