Formula's Summary - Sequence and Series Notes | Study Business Mathematics and Logical Reasoning & Statistics - CA Foundation

1. The general term of an A. P. 

a, a + d, a + 2d, ... is given by t_n = a + (n –1) d

2. S_n, the sum of the first n terms of an A. P.

a, a + d, a + 2d, ...   is given by 

3. A sequence in which the difference of two cousecutive terms is always constant ( ≠ 0) is called an Arithmetic Progression (A. P.)

t_n = S_n – S_n – 1

4. An arithmetic mean between a and b is (a + b)/2

5. A sequence in which the ratio of two consecutive terms is always constant ( ≠ 0) is called a Geometric Progression (G. P.)

6. The nth term of a G.P.: a, ar, ar², ... is ar^{n – 1}

7. Sum of the first n terms of a G. P.: a, ar, ar², ... is

8. The sums of an infintite G. P. a, ar, ar², ... is given by

9. Geometric mean G between two numbers a and b is √ab

10. The arithmetic mean A between two numbers a and b is always greater than the corresponding Geometric mean G  i.e., A > G.