Q. In a series where each term is multiplied by 3 to get the next term, if the first term is 1, what is the 4th term? (2023)
A.
27
B.
81
C.
243
D.
729
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Solution
The series is 1, 3, 9, 27. The 4th term is 27.
Correct Answer:
C
— 243
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Q. In a series where each term is multiplied by 3 to get the next term, starting from 1, what is the 4th term? (2023)
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Solution
The series is 1, 3, 9, 27. The 4th term is 27.
Correct Answer:
A
— 27
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Q. In a series where each term is the square of its position, what is the sum of the first 4 terms? (2023)
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Solution
The first four terms are 1^2, 2^2, 3^2, 4^2 which are 1, 4, 9, 16. Their sum is 1 + 4 + 9 + 16 = 30.
Correct Answer:
B
— 50
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Q. In the series 2, 4, 8, 16, what is the 5th term? (2023)
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Solution
The series is a geometric series with a common ratio of 2. The 5th term is 2 * 2^4 = 32.
Correct Answer:
A
— 32
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Q. In the series 2, 4, 8, 16, what is the pattern followed? (2023)
A.
Addition
B.
Subtraction
C.
Multiplication
D.
Division
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Solution
Each term is obtained by multiplying the previous term by 2, indicating a multiplication pattern.
Correct Answer:
C
— Multiplication
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Q. In the series 2, 5, 10, 17, what is the pattern in the differences between consecutive terms? (2023)
A.
Increasing by 1
B.
Increasing by 2
C.
Increasing by 3
D.
Increasing by 4
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Solution
The differences are 3, 5, 7, which are increasing by 2 each time.
Correct Answer:
C
— Increasing by 3
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Q. In the series 2, 5, 10, 17, what is the pattern used to generate the next term? (2023)
A.
Add consecutive odd numbers
B.
Add consecutive even numbers
C.
Multiply by 2
D.
Subtract 1
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Solution
The pattern is to add consecutive odd numbers: 2 + 3 = 5, 5 + 5 = 10, 10 + 7 = 17. The next term is 17 + 9 = 26.
Correct Answer:
A
— Add consecutive odd numbers
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Q. What is the 4th term of the arithmetic sequence where the first term is 10 and the common difference is -2? (2023)
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Solution
The 4th term is given by a + (n-1)d = 10 + (4-1)(-2) = 10 - 6 = 4.
Correct Answer:
B
— 4
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Q. What is the 4th term of the sequence defined by a_n = n^2 + 2n? (2023)
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Solution
For n = 4, a_4 = 4^2 + 2*4 = 16 + 8 = 24.
Correct Answer:
A
— 24
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Q. What is the 6th term of the sequence defined by a_n = n^2 + n? (2023)
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Solution
For n = 6, a_6 = 6^2 + 6 = 36 + 6 = 42.
Correct Answer:
B
— 42
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Q. What is the 6th term of the sequence defined by a_n = n^2 - n + 1? (2023)
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Solution
Substituting n = 6 gives a_6 = 6^2 - 6 + 1 = 36 - 6 + 1 = 31.
Correct Answer:
C
— 36
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Q. What is the common difference in the arithmetic sequence 10, 15, 20, 25? (2023)
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Solution
The common difference is found by subtracting any two consecutive terms: 15 - 10 = 5.
Correct Answer:
A
— 5
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Q. Which of the following is a characteristic of a converging series? (2023)
A.
It approaches a finite limit
B.
It diverges to infinity
C.
It oscillates indefinitely
D.
It has no limit
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Solution
A converging series approaches a finite limit as more terms are added.
Correct Answer:
A
— It approaches a finite limit
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Q. Which of the following is NOT a characteristic of a Fibonacci sequence? (2023)
A.
Each term is the sum of the two preceding ones.
B.
It starts with 0 and 1.
C.
It can be expressed as a linear function.
D.
It grows exponentially.
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Solution
A Fibonacci sequence cannot be expressed as a linear function; it is defined recursively.
Correct Answer:
C
— It can be expressed as a linear function.
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Q. Which of the following is NOT a characteristic of a geometric sequence? (2023)
A.
Each term is multiplied by a constant.
B.
The ratio between consecutive terms is constant.
C.
The difference between consecutive terms is constant.
D.
It can converge to a limit.
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Solution
In a geometric sequence, the ratio between consecutive terms is constant, not the difference.
Correct Answer:
C
— The difference between consecutive terms is constant.
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Q. Which of the following is NOT a characteristic of a geometric series? (2023)
A.
Each term is multiplied by a constant
B.
The ratio between consecutive terms is constant
C.
The sum of the series can be infinite
D.
The difference between consecutive terms is constant
Show solution
Solution
In a geometric series, the ratio between consecutive terms is constant, not the difference.
Correct Answer:
D
— The difference between consecutive terms is constant
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Q. Which of the following is NOT a property of a geometric series? (2023)
A.
The ratio between consecutive terms is constant
B.
The sum can be infinite
C.
The terms can be negative
D.
The difference between consecutive terms is constant
Show solution
Solution
In a geometric series, the ratio between consecutive terms is constant, not the difference.
Correct Answer:
D
— The difference between consecutive terms is constant
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Q. Which of the following statements about the Fibonacci sequence is true? (2023)
A.
It starts with 0 and 1
B.
It is an arithmetic sequence
C.
It has a constant difference
D.
It is a geometric sequence
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Solution
The Fibonacci sequence starts with 0 and 1, and each subsequent term is the sum of the previous two.
Correct Answer:
A
— It starts with 0 and 1
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Q. Which of the following statements about the sequence defined by a_n = 3n + 1 is true? (2023)
A.
It is an arithmetic sequence.
B.
It is a geometric sequence.
C.
It is a harmonic sequence.
D.
It is a Fibonacci sequence.
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Solution
The sequence defined by a_n = 3n + 1 has a constant difference between consecutive terms, hence it is an arithmetic sequence.
Correct Answer:
A
— It is an arithmetic sequence.
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Q. Which of the following statements about the series 1, 1/2, 1/4, 1/8 is true? (2023)
A.
It is an arithmetic series.
B.
It is a geometric series.
C.
It diverges.
D.
It is a constant series.
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Solution
The series is a geometric series with a common ratio of 1/2.
Correct Answer:
B
— It is a geometric series.
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Q. Which of the following statements about the series 1, 4, 9, 16, 25 is true? (2023)
A.
It is an arithmetic series.
B.
It is a geometric series.
C.
It consists of perfect squares.
D.
It is a Fibonacci series.
Show solution
Solution
The series consists of perfect squares: 1^2, 2^2, 3^2, 4^2, 5^2.
Correct Answer:
C
— It consists of perfect squares.
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Showing 31 to 51 of 51 (2 Pages)
Sequences & Series MCQ & Objective Questions
Understanding Sequences and Series is crucial for students preparing for school and competitive exams in India. This topic not only forms a significant part of the syllabus but also helps in enhancing problem-solving skills. Practicing MCQs and objective questions on Sequences & Series can significantly improve your exam performance and boost your confidence. Dive into our collection of practice questions to master this essential topic!
What You Will Practise Here
Arithmetic Sequences: Definitions, formulas, and examples
Geometric Sequences: Key concepts and calculations
Sum of Sequences: Techniques for finding sums of arithmetic and geometric series
Infinite Series: Understanding convergence and divergence
Special Sequences: Fibonacci and triangular numbers
Applications of Sequences and Series in real-life problems
Common formulas and theorems related to Sequences & Series
Exam Relevance
Sequences and Series are frequently tested in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that require them to identify patterns, calculate sums, or apply formulas. Common question patterns include direct MCQs, fill-in-the-blanks, and problem-solving scenarios that assess conceptual understanding and application skills.
Common Mistakes Students Make
Confusing arithmetic and geometric sequences
Misapplying formulas for the sum of series
Overlooking the importance of initial terms in sequences
Failing to recognize convergence in infinite series
Neglecting to practice different types of problems
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 Sequences & Series for exams?Answer: Regular practice of MCQs and understanding the underlying concepts will greatly enhance your skills.
Don't wait any longer! Start solving our Sequences & Series MCQ questions today to test your understanding and prepare effectively for your exams. Your success is just a practice away!
