(x + y)⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴ Tᵣ₊₁ = ⁿCᵣ · x^{n−r} · y^r r = 0, 1, 2, ..., n Sum of coefficients = 2ⁿ
Σaₙ
Chapter 8  ·  Class XI Mathematics  ·  MCQ Practice

MCQ Practice Arena

Sequences & Series

Pattern Recognition at Speed — AP, GP, HP, and Beyond

📋 50 MCQs ⭐ 50 PYQs ⏱ 75 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
22Easy
18Medium
10Hard
50PYQs
75 secAvg Time/Q
10Topics
Easy 44% Medium 36% Hard 20%

Why Practise These MCQs?

JEE MainJEE AdvancedCBSEBITSATKVPY

Sequences & Series consistently yields 4–6 MCQs in JEE Main — second only to Trigonometry from Class XI. AP-GP-HP combined problems and AM-GM inequality are JEE Advanced staples. KVPY loves elegant AGP and telescoping problems. This is a chapter where speed of formula application determines your score.

Topic-wise MCQ Breakdown

AP — nth Term6 Q
AP — Sum Sₙ6 Q
GP — nth Term5 Q
GP — Sum & Infinite6 Q
HP — nth Term0 Q
AM, GM, HM Relations6 Q
AM-GM Inequality4 Q
AGP0 Q
Special Series Σn, Σn²5 Q
Telescoping Series0 Q
Recurring Decimals (GP)2 Q
Miscellaneous / Mixed10 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$AP: aₙ=a+(n−1)d, Sₙ=n/2[2a+(n−1)d]$
$GP: aₙ=arⁿ⁻¹, S∞=a/(1−r) |r|<1$
$AM≥GM≥HM$
$Σn²=n(n+1)(2n+1)/6$

MCQ Solving Strategy

Identify the progression type in 5 seconds — check ratio for GP, difference for AP, reciprocal-AP for HP. For AM-GM inequality MCQs, express the expression as a sum of terms whose product is constant, then apply AM≥GM directly. For telescoping, write the first 3 and last 2 terms and cancel. Special series Σn, Σn², Σn³ must be memorised cold.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Find nth term and Sₙ of simple AP and GP

② Medium

Combined AP-GP problems, AM-GM applications, HP

③ Hard

AGP sum, telescoping series, three-sequence combined problems

★ PYQ

JEE Main — AM-GM min/max; JEE Advanced — elegant series manipulation

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Straight Lines MCQs
🎯 Knowledge Check

Maths — SEQUENCES AND SERIES

50 Questions Class 11 MCQs
1
Which of the following is an arithmetic sequence?
(CBSE Class XI)
2
The first term of an AP is \(7\) and the common difference is \(3\). Find the second term.
(CBSE Class XI)
3
If the \(n\)th term of an AP is given by \(a_n = 4n + 1\), find its first term.
(CBSE Class XI)
4
Which of the following sequences is decreasing?
(CBSE Class XI)
5
Find the common difference of the AP \(12, 9, 6, 3, …\)
(CBSE Class XI)
6
The 10th term of the AP \(3, 7, 11, …\) is:
(CBSE Class XI)
7
If the first term of an AP is \(a\) and common difference is \(d\), the general term is:
(CBSE Class XI)
8
The sequence defined by \(a_n = 2n^2\) is:
(CBSE Class XI)
9
Find the common ratio of the GP \(2, 6, 18, …\)
(CBSE Class XI)
10
The first term of a GP is \(5\) and the common ratio is \(2\). Find the third term.
(CBSE Class XI)
11
Which of the following is a GP?
(CBSE Class XI)
12
If the common ratio of a GP is \(1\), then the sequence is:
(CBSE Class XI)
13
Find the 5th term of the GP \(1, \frac{1}{2}, \frac{1}{4}, …\)
(CBSE Class XI)
14
Which term of the AP \(7, 13, 19, …\) is \(181\)?
(CBSE Class XI)
15
The arithmetic mean between \(4\) and \(10\) is:
(CBSE Class XI)
16
The geometric mean between \(4\) and \(16\) is:
(CBSE Class XI)
17
If \(A\) and \(G\) are arithmetic and geometric means respectively between two positive numbers, then:
(CBSE Class XI)
18
How many arithmetic means are inserted between \(2\) and \(20\) such that the resulting sequence has 7 terms?
(CBSE Class XI)
19
The sum of the first \(n\) terms of an AP is given by:
(CBSE Class XI)
20
If the sum of first 10 natural numbers is:
(CBSE Class XI)
21
The sum of the first \(n\) terms of a GP is valid only when:
(CBSE Class XI)
22
Find the sum of first 4 terms of the GP \(2, 4, 8, …\)
(CBSE Class XI)
23
The sequence whose \(n\)th term is \(a_n = 5 - 3n\) is:
(CBSE Class XI)
24
If three numbers are in GP and the first is \(a\) and the third is \(b\), then the second is:
(CBSE Class XI)
25
The sequence \(1, -1, 1, -1, …\) is:
(CBSE Class XI)
26
If the \(p\)th term of an AP is \(q\) and the \(q\)th term is \(p\), then the first term is:
(JEE Main)
27
If \(a, b, c\) are in AP, then:
(JEE Main)
28
If \(a, b, c\) are in GP, then:
(JEE Main)
29
The sum of first \(n\) odd natural numbers is:
(CBSE Class XI)
30
The sequence \(2, 5, 10, 17, …\) follows the rule:
(CBSE Class XI)
31
If the sum of the first \(n\) terms of an AP is \(3n^2 + 5n\), then its \(n\)th term is:
(JEE Main)
32
The number of terms in the AP \(7, 13, 19, …, 205\) is:
(JEE Main)
33
If the sum of three consecutive terms of an AP is \(45\), the middle term is:
(CBSE Class XI)
34
The geometric mean of \(a^2\) and \(b^2\) is:
(JEE Main)
35
If the common ratio of a GP is negative, the sequence is:
(CBSE Class XI)
36
Find the sum of first 5 terms of the AP \(2, 7, 12, …\)
(CBSE Class XI)
37
The sequence defined by \(a_n = (-1)^n\) is:
(JEE Main)
38
If the arithmetic mean of two numbers is \(10\) and their geometric mean is \(8\), the numbers are:
(JEE Main)
39
The sum to infinity of the GP \(\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + …\) is:
(CBSE Class XI)
40
If the sum of infinite GP is finite, then:
(CBSE Class XI)
41
The arithmetic mean between two consecutive terms of a GP is always:
(JEE Main)
42
If the 3rd term of a GP is \(8\) and the 5th term is \(32\), then the common ratio is:
(JEE Main)
43
The sum of first \(n\) even natural numbers is:
(CBSE Class XI)
44
If the \(n\)th term of an AP is \(3n - 1\), then its common difference is:
(CBSE Class XI)
45
The sequence whose general term is \(a_n = 5 \cdot 2^{n-1}\) is:
(CBSE Class XI)
46
If the sum of first \(n\) terms of a GP is \(S_n\), then \(S_{n+1} - S_n\) equals:
(JEE Main)
47
If three numbers are in AP and their product is \(64\), the middle number is:
(JEE Main)
48
The sequence \(1, 1, 2, 3, 5, 8, …\) is:
(CBSE Class XI)
49
If the first term of a GP is \(a\) and the sum to infinity is \(S\), then the common ratio is:
(JEE Main)
50
If the arithmetic mean between two numbers exceeds their geometric mean by \(2\), then:
(JEE Advanced)
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Frequently Asked Questions

A sequence is an ordered list of numbers written according to a definite rule, where each number is called a term of the sequence.

In a sequence, order matters and repetition is allowed, whereas in a set order does not matter and repetition is not allowed.

The nth term is the general term of a sequence that represents the term at position \(n\).

A finite sequence has a limited number of terms, such as \(2,4,6,8\).

An infinite sequence has infinitely many terms, such as \(1,2,3,\dots\).

A series is the sum of the terms of a sequence.

A sequence lists terms, while a series represents their sum.

An arithmetic progression is a sequence in which the difference between consecutive terms is constant.

The common difference \(d\) is the difference between any term and its preceding term.

The general form of an AP is \(a, a+d, a+2d, a+3d, \dots\).

The nth term of an AP is given by \(a_n = a + (n-1)d\).

The symbol \(a\) represents the first term of the arithmetic progression.

The common difference is found by dividing the difference of the terms by the difference of their positions.

An arithmetic mean is a number inserted between two numbers such that all three form an AP.

The arithmetic mean is \(\dfrac{a+b}{2}\).

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