# Sequence and Series Formula List For Bank Exams: Check and Download PDF Examples Sheet

Sequence and Series Formula PDF For Bank Exams: Sequence and Series Formula PDF contains the Sequence and Series topics from basic to advanced level. Sequence and Series is one of the important basic arithmetic topics in Mathematics. When a collection of elements follows a pattern that is said to be a Sequence and the sum of all the elements in the sequence is said to be a Series. While calculating the series, all the terms must have a definite relationship between them. The sequence formula is formed with the use of the nth term and the series is formed with the sum. By understanding the basics the candidates can easily solve the problems based on the topic. A basic understanding of the problem fundamentals is mainly based on the formulas given for the specific topic. While calculating the sequence, the length of the sequence is equal to the number of terms which can be finite or infinite. This is explained well in sequence and series formula class 11 Maths, sequence and series formula class 12 Maths.

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## Sequence and Series Formula Sheet PDF For Bank Exams

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## What is Sequence and Series?

Here we have provided a detailed explanation of the Sequence and Series in this Sequence and Series Formulas PDF. In most of the bank exams, we are required to solve the questions within an allotted time with speed and accuracy. So for that, you can use this Sequence and Series Formulas PDF to solve any level of questions with speed and accuracy. Candidates shall go through this Sequence and Series Formula PDF Download to know more about the Sequence and Series topic.

Sequence: A sequence is a collection of objects/elements in a particular order based on some rule. If a1, a2, a3, a4,……… etc. denote the terms of a sequence, then 1,2,3,4,…..denotes the position of the term.

A sequence can be identified based on the number of terms i.e. either finite sequence or infinite sequence.

Finite:- If a sequence has an end element, then it is called a Finite Sequence.

For example, (1,3,5,7,9,11,13)

Infinite:- If a sequence continues with endless terms then it is called an infinite sequence.

For example, ( 1,2,3,4,5,6,7,......)

Series: A series can be defined as the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence.

If a1, a2, s3, a4,.......is a sequence then the series will be a1+a2+a3+a4+..........

## Difference Between Sequence and Series

The difference between the Sequence and Series is added in the table given below in this Sequence and Series Formula for Bank exams article. To know the difference between the Sequence and Series is more important while solving the Sequence and Series problems by using this Sequence and Series Formulas. The Sequence and Series Formulas PDF will help you for your future reference.

### Difference Between Sequence and Series

#### Series

The set of elements follows a certain pattern in sequence

The sum of elements of the sequence is called a series

Order of the elements is significant

Order of the elements is not so important

Finite sequence: 6,7,8,9,10

Finite sequence 5+7+8+9+!0

Infinite Sequence 4,5,6,7,8,.......

Infinite sequence 4+5+6+7+8+.....

## Types of Sequence and Series Formula For Bank Exams

Here we have provided some of the most common types of Sequence and Series. Aspirants can make use of this Sequence and Series Formula post to know the types of Sequences and Series in the Bank exams.

• Arithmetic Sequences
• Geometric Sequences
• Harmonic Sequences
• Fibonacci Numbers

Arithmetic sequence:- If the difference between the term and its previous term is always the same, that type of series is called an arithmetic sequence. Every term in a sequence is created by adding or subtracting a definite number from the previous number is an arithmetic sequence.

a, a+d, a+2d,……,a+(n-1)d,….

Geometric Sequence: A geometric series is a sequence where every successive term has a fixed ratio between them is called a geometric sequence. A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number is known as a geometric sequence.

a, ar, ar2,….,ar(n-1),…

Harmonic Sequence:- When the reciprocals of all the numbers or elements form an arithmetic sequence then it is called a harmonic sequence.

1/a, 1/(a+d), 1/(a+2d), 1/(a+3d), 1/(a+4d), ....,

Fibonacci Numbers:- A form of a sequence of numbers in which each component is found by adding two preceding elements and the sequence starts with 0 and 1.

F0 = 0 and F1 = 1 and Fn = Fn-1 + Fn-2

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## Arithmetic Sequence and Series Formula For Bank Exams

The arithmetic Sequence and Series Formulas are provided in the table given below. Candidates can go through this table to learn more about arithmetic Sequence and Series Formulas for Bank exams. The aspirants should memorize the important Sequence and Series Formulas to improve their ability to solve any type of Sequence and Series Problems with the Sequence and Series formulas.

### Arithmetic Sequence and Series Formulas

#### Arithmetic Sequence and Series Formula

Sequence

a, a+d, a+2d,……,a+(n-1)d,….

Common Difference or Ratio

Successive term – Preceding term

Common difference = d = a2 – a1

General Term (nth Term)

an = a + (n-1)d

nth term from the last term

an = l – (n-1)d

Sum of first n terms

sn = n/2(2a + (n-1)d)

## GeometricSequence and Series Formula For Bank Exams

The Geometric Sequence and Series Formula for Bank exams are provided in the table given below. Aspirants shall go through this table to learn more about geometric Sequence and Series Formulas. You must memorize the important geometric Sequence and Series Formulas to score good marks in this topic.

### Geometric Sequence and Series Formulas

#### Geometric Sequence and Series Formula

Sequence

a, ar, ar2,….,ar(n-1),…

Common Difference or Ratio

Successive term/Preceding term

Common ratio = r = ar(n-1)/ar(n-2)

General Term (nth Term)

an = ar(n-1)

nth term from the last term

an = l/r(n-1)

Sum of first n terms

sn = a(1 – rn)/(1 – r) if |r| < 1

sn = a(rn -1)/(r – 1) if |r| > 1

## Sequence and Series Formulas and Examples

In this Sequence and Series Formula for Bank exams post, we have provided some Sequence and Series Formulas and examples. Candidates can practice more types of Sequence and Series Problems by exploiting the Sequence and Series Formula PDF Download. This Sequence and Series Formulas PDF also has the Sequence and Series Formulas with examples. You can solve the questions related to this Sequence and Series Formulas and examples by making use of the Sequence and Series Formulas PDF.

Example 1: Find the sum of the first 100 terms of the arithmetic series 1 + 4 + 7 +...

Solution:

In the given series, the first term is a = 1 and the common difference is d = 3.

Using the sequences and series formulas,

Sn = n/2 (2a + (n - 1) d)

For the sum of 100 terms, substitute n = 100:

S100 = 100/2 (2(1) + (100 - 1) 3) = 14,950

Answer: The sum of the first 100 terms is 14,950.

Example 2: If 4,7,10,13,16,19,22……is a sequence, Find:

a) Common difference

b) nth term

Solution: Given sequence is, 4,7,10,13,16,19,22……

a) The common difference = 7 – 4 = 3

b) The nth term of the arithmetic sequence is denoted by the term Tn and is given by Tn = a + (n-1)d, where “a” is the first term and d is the common difference.

Tn = 4 + (n – 1)3 = 4 + 3n – 3 = 3n + 1

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## Sequence and Series Formula For Bank Exams - FAQs

Q. What is the formula to find nth term in an arithmetic sequence?

A. nth term from the last term = an = l – (n-1)d

Q. What is Harmonic Sequence?

A. When the reciprocals of all the numbers or elements forms an arithmetic sequence then it is called as harmonic sequence.

1/a, 1/(a+d), 1/(a+2d), 1/(a+3d), 1/(a+4d), ....,

Q. What is the formula to find Common Difference or Ratio in Geometric Sequence?

A. Common Difference or Ratio = Successive term/Preceding term

Common ratio = r = ar(n-1)/ar(n-2)

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