JEE Main Eligibility Criteria 2025- Marks in Class 12th, Age Limit

# Sequence And Series - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• Sequences, Series and Progression is considered one of the most asked concept.

• 25 Questions around this concept.

## Solve by difficulty

Statement 1:The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... + (361 + 380 +400) is 8000.

Statement  2: $\dpi{100} \sum_{k=1}^{n}\left ( k^{3} -\left ( k-1 \right )^{3}\right )=n^{3}$ for any natural number n.

## Concepts Covered - 1

Sequences, Series and Progression

Sequences:

A sequence is formed when terms are written in order such that they follow a particular pattern

Eg, 1, 2, 3, 4, 5,.....

1, 4, 9, 16, ......

1/3, 1/4, 1/5, 1/6, ......

Finite and Infinite Sequences

A sequence may have an infinite number of terms or a finite number of terms.

If a sequence has three dots at the end, then it indicates the list never ends. It has infinite numbers of terms. Then, the sequence is said to be an infinite sequence.

Eg, 2, 4, 6, 8, 10, …

If sequence has only a finite number of terms, then the sequence is called a finite sequence.

Eg, 2, 4, 6, 8

5, 8, 11, 14, ......., 65

nth term

In sequences nth term is usually denoted by an or tn or Tn

So, in sequence 2, 4, 6, 8, ...

a1= 2, a2= 4, a3= 6, and so on

We can write it in compact form as an = 2n

an or nth term is also called General term of the sequence.

So a sequence can be written as a1, a2, a3, ........

Conversely, if the general term of a sequence is given, we can find any term of that sequence.

Eg, If T= 2n , then fourth term can be obtained by putting n = 4

So, T4 = 24 = 16

Series:

If we add or subtract all the terms of a sequence we will get an expression, which is called a series. It is denoted by Sn.$\\\mathrm{If\;the\;sequence\;is\;\mathit{a_1,a_2,a_3,......,a_n},\;\;then\;it's\;sum\;i.e.\;\mathit{a_1+a_2+a_3+...........+a_n} } \\\mathrm{is\;a\;series.}$

$\\\mathrm{S_n=\mathit{a_1+a_2+a_3+...........+a_n} =\sum_{r=1}^n\mathit{a_r}=\sum\mathit{a_r}}\\\mathrm{Then,}\\\mathrm{\;S_n-S_{n-1}=\left ( \mathit{a_1+a_2+a_3+...........+a_{n-1}+a_n} \right )}\\\mathrm{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;-\left ( \mathit{a_1+a_2+a_3+...........+a_{n-1}} \right )}\\\mathrm{Thus,\;\;\;\mathit{a_n}=S_n-S_{n-1}}$

This is the formula for finding general term of a sequence if the sum of n terms is given.

Progression:

If the terms of a sequence follow some pattern that can be defined by an explicit formula in n, then the sequence is called a progression.

Eg. 3, 9, 27, 81…

Here, general term can be written explicitly in terms of n, which is 3n

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Sequences, Series and Progression

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## Books

### Reference Books

#### Sequences, Series and Progression

Mathematics for Joint Entrance Examination JEE (Advanced) : Algebra

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