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## Maths Chapter 8 Sequence and Series Class 11 MCQs

Improve your grasp of **sequences and series** with our detailed **MCQs for Class 11 Mathematics Chapter 8.** This chapter covers essential concepts like sequences, types of series, and their applications, making it a crucial part of your maths curriculum. Our **Sequence and Series class 11 MCQs** are designed to help you understand arithmetic and geometric progressions, ensuring you are well-prepared and confident in your studies.

Our collection of **sequence and series class 11 MCQs with answers **covers a wide range of topics, from basic sequences to complex series calculations. Each question aligns with the Class 11 **CBSE syllabus**, providing a valuable resource for revision and practice. Prepare effectively for your exams with our MCQs, which enhance your learning and boost your academic performance. You can also download **NCERT solutions for Class 11 Mathematics** to further solidify your understanding of the concepts.

## Sequence and Series Class 11 MCQ Questions with Answers

Here are the important sequence and series class 11 MCQ questions with answers:

- What is the common difference in the arithmetic sequence: 5, 10, 15, 20?
- a) 3
- b) 5
- c) 10
- d) 15

**Answer: b) 5** - In the sequence \(2, 4, 8, 16, \ldots\), what is the common ratio?
- a) 2
- b) 4
- c) 8
- d) 16

**Answer: a) 2** - If the nth term of an arithmetic progression is given by \(a_n = 3n + 2\), what is the first term?
- a) 2
- b) 3
- c) 5
- d) 6

**Answer: c) 5** - What is the sum of the first 5 terms of the arithmetic sequence \(3, 7, 11, 15, \ldots\)?
- a) 35
- b) 40
- c) 45
- d) 50

**Answer: d) 50** - The 5th term of a geometric progression is 81 and the common ratio is 3. What is the first term?
- a) 3
- b) 9
- c) 27
- d) 1

**Answer: d) 1** - In the arithmetic sequence \(a, a+d, a+2d, \ldots\), if \(a = 2\) and \(d = 3\), what is the 7th term?
- a) 20
- b) 21
- c) 22
- d) 23

**Answer: b) 21** - Which of the following represents a geometric sequence?
- a) \(1, 2, 3, 4, \ldots\)
- b) \(2, 4, 8, 16, \ldots\)
- c) \(5, 10, 15, 20, \ldots\)
- d) \(1, 3, 5, 7, \ldots\)

**Answer: b) 2, 4, 8, 16, \ldots** - Find the sum of the first 10 terms of the geometric sequence \(3, 6, 12, 24, \ldots\)
- a) 3069
- b) 3070
- c) 3071
- d) 3072

**Answer: d) 3072** - If the 3rd term of a geometric progression is 18 and the 6th term is 486, what is the common ratio?
- a) 2
- b) 3
- c) 4
- d) 5

**Answer: b) 3** - What is the arithmetic mean (A.M.) of 6 and 10?
- a) 7
- b) 8
- c) 9
- d) 10

**Answer: b) 8** - What is the geometric mean (G.M.) of 4 and 16?
- a) 8
- b) 10
- c) 12
- d) 14

**Answer: a) 8** - If the first term of a geometric sequence is 7 and the common ratio is 2, what is the 5th term?
- a) 56
- b) 112
- c) 224
- d) 448

**Answer: c) 224** - Find the sum of the first 5 terms of the geometric sequence \(1, \frac{1}{2}, \frac{1}{4}, \ldots\)
- a) \(\frac{31}{32}\)
- b) \(\frac{32}{31}\)
- c) \(\frac{33}{32}\)
- d) \(\frac{32}{33}\)

**Answer: a) \(\frac{31}{32}\)** - What is the sum of the first 15 natural numbers?
- a) 120
- b) 105
- c) 115
- d) 110

**Answer: b) 105** - If \(a = 5\) and \(d = 3\) in an arithmetic sequence, what is the sum of the first 20 terms?
- a) 480
- b) 510
- c) 520
- d) 530

**Answer: c) 520** - In the sequence \(2, 6, 18, 54, \ldots\), what is the 6th term?
- a) 162
- b) 324
- c) 486
- d) 972

**Answer: c) 486** - Which term of the arithmetic sequence \(3, 6, 9, 12, \ldots\) is 60?
- a) 18th
- b) 19th
- c) 20th
- d) 21st

**Answer: b) 19th** - If the sum of the first n terms of a sequence is given by \(S_n = n^2 + 2n\), what is the 5th term?
- a) 15
- b) 17
- c) 19
- d) 21

**Answer: c) 19** - If the sum of the first 6 terms of a geometric sequence is 63 and the first term is 1, what is the common ratio?
- a) 2
- b) 3
- c) 4
- d) 5

**Answer: a) 2** - What is the sum of the squares of the first 10 natural numbers?
- a) 285
- b) 385
- c) 485
- d) 585

**Answer: b) 385** - The nth term of a sequence is given by \(a_n = 4n – 3\). What is the 10th term?
- a) 37
- b) 38
- c) 39
- d) 40

**Answer: a) 37** - If the first term of an arithmetic sequence is 2 and the 10th term is 20, what is the common difference?
- a) 1.5
- b) 2
- c) 2.5
- d) 3

**Answer: b) 2** - In the sequence \(1, 4, 9, 16, \ldots\), what is the general term \(a_n\)?
- a) \(n^2\)
- b) \(n^2 – 1\)
- c) \(n^2 + 1\)
- d) \(n^2 + 2\)

**Answer: a) \(n^2\)** - What is the sum of the first 8 terms of the sequence \(5, 10, 15, 20, \ldots\)?
- a) 120
- b) 140
- c) 160
- d) 180

**Answer: c) 160** - If the 5th term of a geometric progression is 243 and the common ratio is 3, what is the 1st term?
- a) 1
- b) 3
- c) 9
- d) 27

**Answer: b) 3** - The sum of the first n terms of an arithmetic sequence is given by \(S_n = 3n^2 + n\). What is the first term?
- a) 4
- b) 5
- c) 6
- d) 7

**Answer: b) 4** - What is the sum of the cubes of the first 5 natural numbers?
- a) 225
- b) 275
- c) 300
- d) 225

**Answer: d) 225** - If the nth term of an arithmetic progression is given by \(a_n = 2n + 1\), what is the 15th term?
- a) 29
- b) 30
- c) 31
- d) 32

**Answer: a) 29** - If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 8th term?
- a) 384
- b) 512
- c) 768
- d) 1024

**Answer: a) 384** - In the sequence \(5, 15, 45, \ldots\), what is the 7th term?
- a) 3645
- b) 7290
- c) 10935
- d) 14580

**Answer: a) 3645** - What is the arithmetic mean (A.M.) of 12 and 18?
- a) 14
- b) 15
- c) 16
- d) 17

**Answer: b) 15**

### Important Topics Included in Class 11 Maths Chapter 8 Sequence and Series

- Introduction to Sequences and Series:
- Arithmetic Progression (AP)
- Geometric Progression (GP)
- Special Series
- Relationship Between A.M. and G.M.
- Finite and Infinite Sequences
- Fibonacci Sequence
- Sigma Notation
- Miscellaneous Problems and Applications

## FAQs on Class 11 Maths Chapter 8 Sequence and Series MCQs

### Who invented sequence?

The concept of sequences and series has been around for thousands of years, with ancient mathematicians like Euclid and Archimedes contributing to its development. However, the modern understanding of sequences and series was formalized by mathematicians like Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century.

### What is series used for?

Series are used in various fields like mathematics, physics, engineering, and economics to model real-world phenomena. They are used to represent the sum of an infinite number of terms, which can be used to solve problems in fields like calculus, differential equations, and probability theory.

### What is the purpose of series and sequences?

The primary purpose of sequences and series is to model and analyze real-world phenomena that involve infinite or infinite sums of terms. They are used to solve problems in various fields, including mathematics, physics, engineering, and economics.

### What are the four types of sequences?

The four main types of sequences are arithmetic, geometric, harmonic, and Fibonacci sequences. Arithmetic sequences involve adding a fixed constant to each term, geometric sequences involve multiplying each term by a fixed constant, harmonic sequences involve the reciprocals of the terms, and Fibonacci sequences involve the sum of the previous two terms.

### What are the applications of sequence and series?

Sequences and series have numerous applications in various fields, including mathematics, physics, engineering, and economics. They are used to model population growth, electrical circuits, and financial markets, among other things. They are also used in computer programming and data analysis.

### What is the difference between sequence and series?

A sequence is a list of terms in a specific order, while a series is the sum of the terms in a sequence. In other words, a sequence is a list of numbers, while a series is the total value of those numbers.