# How to solve number series problems quickly

In banking exams, there are so many important topics but in that Number series is one of the main topics. In this article, we are sharing a way How to solve number series problems quickly. A sequence is an arrangement of any set of numbers in a particular order followed by some rule.

## There are four types of sequence in number series

1. Arithmetic sequence: The sequence consists of every term is created by adding or subtracting a definite number to the preceding number is known as Arithmetic sequence
2. Geometric sequence: The sequence consists of every term is obtained by multiplying or dividing a definite number with the preceding number is known as the Geometric sequence.
3. Harmonic sequence: A series of numbers is known as a harmonic sequence if the reciprocals of all the elements of the sequence.
4. Fibonacci sequence: Fibonacci number forms an interesting sequence of numbers in which each element is obtained by adding two preceding elements and the sequence starts with 0 and 1.

In Arithmetic progression

• sequence  formula is a,a+d,a+2d , ………a+(n-1)d
• common difference  formula is Successive term -preceding term

common difference =d=a2 – a1

• general term is A n=a+(n-1)d
• nth term from last term is A n=1-(n-1)d
• sum of first n terms is S n =n/2(2a+(n-1)d)

In Geometric progression

• sequence formula is a,ar ,ar .r ,…………..
• common difference formula is Successive term/preceding term

Sequence is a set of elements that follow a pattern .Each number in a sequence is called a term. In sequence order of element is important.Finite sequence is 1,2,3,4,5 and Infinite sequence is 1,2,3,4……..

Series is the sum of elements of the sequence. The finite series is 1+2+3+4+5. Infinite series is 1+2+3+4+……

To get knowledge of number series candidates should learn squares of numbers up to 40 and cubes of numbers up to 20

• Based on addition and subtraction: For example, the sequence is 2,6,10,15,18,22 .the difference between two successive numbers is 4 but between 10 and 15 it is 5 and between 15 and 18 it is 3 .so the wrong answer is 15 and the correct answer is 14
• Based on multiplication and division: In this, we should check the difference between two successive numbers that it is half of the previous number as per the problem.
• Based on squares and cubes: for example, the sequence is 8 27 125 512 1331 2197

in this 2 cube is 8

3 cube is 27

5 cube is 125

8 cube is 512

11 cube is  1331

13 cube is 2197. In this solution, all numbers are prime except 8  so in the place of 8                         there should be 7 cubes i.e..,343

• Based on the mixed pattern: There are two patterns

Pattern 1:The difference of 5 10 19 41 80. In this, the difference is 2 times of the previous one. but 19 and 41 are not a correct pattern.in place of 41, we can replace 40 to correct the sequence.

Pattern 2 is different from pattern 2 because it is of multiplying term and subtracting 1 from it and by doing this if the sequence is incorrect we should check and replace the numbers.

By all logic and tricks  above candidates can solve number series problems easily.