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