SEQUENCES and SERIES formulas
SEQUENCES and SERIES Formulas Sequences :- A finite sequence is a sequence that contains the last term such as a 1 , a 2 , a 3 , a 4 , a 5 , a 6 ……a n. On the other hand, an infinite sequence is never-ending i.e. a 1 , a 2 , a 3 , a 4 , a 5 , a 6 ……a n…. . AP a 1 , a 2 , a 3 , a 4 , a 5 , a 6 ……a n…. . GP:- a, ar, ar 2 , ar 3 , ar 4 ,…,a n Arithmetic Progression In AP, we will come across three main terms, which are denoted as: Common difference (d) nth Term (a n ) Sum of the first n terms (S n ) Nth term of sequence is a + (n – 1) d, a n = a + (n − 1) × d Geometric Progression :- General Form of GP The general form of Geometric Progression is: a, ar, ar 2 , ar 3 , ar 4 ,…,a n Where, a = First term r = common ratio a n = nth term Formula :- a n = ar n-1 To find the sum of the first n terms of a geometric sequence(G.P) sequence. use the formula, S n = a 1 ( 1 − r n ) 1 − r , r ≠ 1 where n is the numb...