Sequences & Series for Competitive Exam Preparation

Sequences & Series

Q. Find the sum of the first 15 terms of the geometric series where the first term is 2 and the common ratio is 3.

A. 143
B. 145
C. 146
D. 147

Solution

The sum of the first n terms of a geometric series is S_n = a(1 - r^n) / (1 - r). Here, a = 2, r = 3, n = 15. So, S_15 = 2(1 - 3^15) / (1 - 3) = 2(1 - 14348907) / -2 = 14348906.

Correct Answer: C — 146

Learn More →

Q. Find the sum of the first 5 terms of the series 1, 4, 9, 16, ...

A. 30
B. 31
C. 32
D. 33

Solution

The series is the sum of squares: 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 1 + 4 + 9 + 16 + 25 = 55.

Correct Answer: B — 31

Learn More →

Q. If the first term of a geometric series is 4 and the common ratio is 2, what is the 7th term?

A. 128
B. 256
C. 512
D. 1024

Solution

The nth term of a geometric series is given by a_n = ar^(n-1). Here, a = 4, r = 2, n = 7. So, a_7 = 4 * 2^(7-1) = 4 * 64 = 256.

Correct Answer: B — 256

Learn More →

Q. If the first term of an arithmetic series is 12 and the last term is 48, what is the common difference if there are 10 terms?

A. 4
B. 3
C. 5
D. 6

Solution

In an arithmetic series, the last term can be expressed as a + (n-1)d. Here, 48 = 12 + (10-1)d. Thus, 48 - 12 = 9d, giving d = 4.

Correct Answer: A — 4

Learn More →

Q. In a sequence where the nth term is given by n^2 + 2n, what is the 6th term?

A. 48
B. 50
C. 52
D. 54

Solution

Substituting n = 6 into the formula: a_6 = 6^2 + 2(6) = 36 + 12 = 48.

Correct Answer: A — 48

Learn More →

Q. What is the 10th term of the arithmetic sequence where the first term is 5 and the common difference is 3?

A. 32
B. 35
C. 30
D. 28

Solution

The nth term of an arithmetic sequence is given by a_n = a + (n-1)d. Here, a = 5, d = 3, n = 10. So, a_10 = 5 + (10-1) * 3 = 5 + 27 = 32.

Correct Answer: B — 35

Learn More →

Q. What is the 12th term of the arithmetic sequence where the first term is 7 and the common difference is 5?

A. 62
B. 67
C. 72
D. 77

Solution

Using the formula a_n = a + (n-1)d, we have a_12 = 7 + (12-1) * 5 = 7 + 55 = 62.

Correct Answer: A — 62

Learn More →

Q. What is the 5th term of the sequence defined by a_n = 2n^2 + 3n - 1?

A. 45
B. 47
C. 49
D. 51

Solution

To find the 5th term, substitute n = 5 into the formula: a_5 = 2(5^2) + 3(5) - 1 = 2(25) + 15 - 1 = 50 + 15 - 1 = 64.

Correct Answer: B — 47

Learn More →

Q. What is the 8th term of the sequence defined by a_n = 3n - 2?

A. 22
B. 24
C. 26
D. 28

Solution

Substituting n = 8 into the formula: a_8 = 3(8) - 2 = 24 - 2 = 22.

Correct Answer: A — 22

Learn More →

Showing 1 to 9 of 9 (1 Pages)

Sequences & Series MCQ & Objective Questions

Understanding Sequences and Series is crucial for students preparing for school exams and competitive tests in India. This topic not only forms a significant part of the syllabus but also helps in developing analytical skills. Practicing MCQs and objective questions related to Sequences and Series can greatly enhance your exam preparation, ensuring you grasp important concepts and score better in your assessments.

What You Will Practise Here

Definition and types of sequences: arithmetic, geometric, and harmonic.
Understanding series and their convergence.
Key formulas related to the sum of sequences and series.
Finding the nth term of a sequence.
Applications of sequences and series in real-life problems.
Common patterns in sequences and series problems.
Diagrams and visual aids to understand concepts better.

Exam Relevance

Sequences and Series are frequently tested in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that require them to identify patterns, calculate sums, or apply formulas. Common question patterns include multiple-choice questions that assess both conceptual understanding and problem-solving skills. Mastery of this topic can significantly impact your overall performance in these competitive exams.

Common Mistakes Students Make

Confusing the terms 'sequence' and 'series'.
Overlooking the importance of the common difference in arithmetic sequences.
Misapplying formulas for the sum of series.
Failing to recognize patterns in complex sequences.
Neglecting to check for convergence in infinite series.

FAQs

Question: What are the key differences between sequences and series?
Answer: A sequence is a list of numbers in a specific order, while a series is the sum of the terms of a sequence.

Question: How can I improve my skills in solving Sequences & Series MCQs?
Answer: Regular practice of objective questions and understanding the underlying concepts will help improve your skills significantly.

Question: Are there any specific formulas I should memorize for this topic?
Answer: Yes, key formulas for the sum of arithmetic and geometric series are essential to memorize for quick problem-solving.

Now is the time to boost your confidence and understanding of Sequences and Series. Dive into our practice MCQs and test your knowledge to excel in your exams!

Sequences & Series

Sequences & Series MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?