Welcome To My School Study
Practice Class 10 Maths Chapter 5 Arithmetic Progressions MCQs with answers, formulas and detailed solutions based on the NCERT syllabus.
Do You Know
Chapter Information
- Subject: Mathematics
- Class: 10
- Chapter: Arithmetic Progressions
- Question Type: MCQs
- Practice Set: 1
- Difficulty Level: Easy to Moderate
- Based On: NCERT Class 10 Mathematics Syllabus
Introduction
Arithmetic Progressions (AP) are an important topic in Class 10 Mathematics. An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms remains constant.
In this practice set, you will work with basic concepts of arithmetic progressions, including identifying an AP, finding the common difference, calculating the nth term, finding the position of a particular term, and calculating the sum of the first few terms.
What You Will Learn?
After completing this practice set, you will be able to:
- Identify an arithmetic progression.
- Find the common difference of an AP.
- Use the formula for the nth term.
- Find the position of a given term.
- Calculate the sum of the first n terms.
- Apply AP formulas correctly in examination questions.
Why This Topic Is Important?
Arithmetic Progressions are an important part of the Class 10 Mathematics syllabus. Questions based on the nth term, common difference and sum of terms are commonly used to test students’ understanding of sequences and algebraic formulas.
A clear understanding of AP formulas also helps students solve numerical and application-based questions more efficiently.
Exam Relevance
Students should remember the standard formulas of Arithmetic Progressions and understand when to use each formula. MCQs can test concepts as well as direct numerical calculations.
Important areas include:
- First term
- Common difference
- nth term
- Number of terms
- Sum of n terms
- Last term
MCQs with Detailed Solutions
Q1. Which of the following sequences is an Arithmetic Progression?
A) 2, 5, 8, 11, 14
B) 2, 5, 9, 14, 20
C) 1, 3, 6, 10, 15
D) 4, 8, 16, 32, 64
Answer: A) 2, 5, 8, 11, 14
Useful Concept
A sequence is an Arithmetic Progression if the difference between consecutive terms is constant.
Solution
For option A:
$$5-2=3$$
$$8-5=3$$
$$11-8=3$$
$$14-11=3$$
The common difference is always 3.
Therefore, the sequence is an Arithmetic Progression.
Correct Answer: A
Q2. What is the common difference of the AP 7, 12, 17, 22, …?
A) 3
B) 4
C) 5
D) 6
Answer: C) 5
Useful Concept
The common difference of an AP is found by subtracting one term from the next consecutive term.
Solution
Given AP:
$$7,12,17,22,\ldots$$
Therefore:
$$d=12-7$$
$$d=5$$
We can also verify:
$$17-12=5$$
$$22-17=5$$
Hence, the common difference is 5.
Correct Answer: C
Q3. Find the 8th term of the AP 3, 7, 11, 15, …
A) 27
B) 31
C) 35
D) 39
Answer: B) 31
Useful Concept
The nth term of an AP is given by:
$$a_n=a+(n-1)d$$
Solution
Given:
$$a=3$$
$$d=7-3$$
$$d=4$$
and:
$$n=8$$
Using the nth-term formula:
$$a_n=a+(n-1)d$$
Therefore:
$$a_8=3+(8-1)(4)$$
$$a_8=3+7\times4$$
$$a_8=3+28$$
$$a_8=31$$
Therefore, the 8th term is 31.
Correct Answer: B
Q4. Which term of the AP 5, 9, 13, 17, … is 41?
A) 8th term
B) 9th term
C) 10th term
D) 11th term
Answer: C) 10th term
Useful Concept
The nth term of an AP is:
$$a_n=a+(n-1)d$$
Solution
Given:
$$a=5$$
$$d=9-5$$
$$d=4$$
The required term is:
$$a_n=41$$
Using the formula:
$$41=5+(n-1)4$$
Subtract 5 from both sides:
$$41-5=4(n-1)$$
$$36=4(n-1)$$
Divide both sides by 4:
$$\frac{36}{4}=n-1$$
$$9=n-1$$
Therefore:
$$n=10$$
Hence, 41 is the 10th term of the AP.
Correct Answer: C
Q5. Find the sum of the first 10 terms of the AP 2, 5, 8, 11, …
A) 145
B) 150
C) 155
D) 160
Answer: C) 155
Useful Concept
The sum of the first n terms of an AP is:
$$S_n=\frac{n}{2}[2a+(n-1)d]$$
Solution
Given:
$$a=2$$
$$d=5-2$$
$$d=3$$
$$n=10$$
Using the sum formula:
$$S_{10}=\frac{10}{2}[2(2)+(10-1)(3)]$$
$$S_{10}=5[4+9(3)]$$
$$S_{10}=5[4+27]$$
$$S_{10}=5\times31$$
$$S_{10}=155$$
Therefore, the sum of the first 10 terms is 155.
Correct Answer: C
Important Formulas & Concepts
1. General Form of an AP
An arithmetic progression can be written as:
$$a,\ a+d,\ a+2d,\ a+3d,\ldots$$
Here, $$a$$ is the first term and $$d$$ is the common difference.
2. Common Difference
$$d=a_2-a_1$$
The common difference is the difference between any two consecutive terms.
3. nth Term of an AP
$$a_n=a+(n-1)d$$
4. Sum of First n Terms
$$S_n=\frac{n}{2}[2a+(n-1)d]$$
5. Sum Using the Last Term
If the last term is $$l$$, then:
$$S_n=\frac{n}{2}(a+l)$$
6. Three Consecutive Terms in an AP
If three numbers $$a$$, $$b$$, and $$c$$ are consecutive terms of an AP, then:
$$2b=a+c$$
Related Practice Questions
Try solving these questions yourself:
- Determine whether 4, 9, 14, 19, 24 is an AP.
- Find the common difference of 15, 11, 7, 3, …
- Find the 12th term of the AP 6, 10, 14, 18, …
- Which term of the AP 8, 13, 18, 23, … is 58?
- Find the sum of the first 15 terms of the AP 3, 6, 9, 12, …
Mini Quiz Challenge
Test your understanding:
1. What is the common difference of 10, 15, 20, 25, …?
2. Find the 6th term of the AP 4, 7, 10, 13, …
3. Is 2, 4, 7, 10, … an AP?
4. Find the first term of an AP if its 5th term is 18 and common difference is 3.
5. Find the sum of the first 5 terms of the AP 1, 4, 7, 10, …
Exam Tips
- Always identify the first term $$a$$ and common difference $$d$$ before applying a formula.
- Check whether the difference between consecutive terms is constant.
- Use the nth-term formula carefully when finding the position of a term.
- For sum questions, identify $$n$$, $$a$$, and $$d$$ clearly.
- Be careful with the expression:
$$$(n-1)d$$
- Check your final answer using the original AP whenever possible.
- Practice both direct formula-based and application-based AP questions.
Quick Revision Notes
- An AP has a constant difference between consecutive terms.
- The first term is represented by $$a$$.
- The common difference is represented by $$d$$.
- nth term:
$$a_n=a+(n-1)d$$
- Sum of first $$n$$ terms:
$$S_n=\frac{n}{2}[2a+(n-1)d]$$
- If the last term is $$l$$:
$$S_n=\frac{n}{2}(a+l)$$
- For three consecutive AP terms:
$$2b=a+c$$
Common Mistakes Students Make
- Using $$n$$ instead of $$(n-1)$$ in the nth-term formula.
- Finding the common difference with the wrong order of subtraction.
- Forgetting to identify the first term before using an AP formula.
- Using the sum formula when the question asks only for a particular term.
- Making calculation errors while substituting values.
- Assuming a sequence is an AP without checking its consecutive differences.
Key Takeaways
- Arithmetic Progression is a sequence with a constant common difference.
- The nth-term formula helps find any specific term of an AP.
- The sum formula helps calculate the sum of the first $$n$$ terms.
- Correct identification of $$a$$, $$d$$, and $$n$$ is essential for solving AP questions.
- Regular practice improves speed and accuracy in board examinations.
FAQs
Q1. What is an Arithmetic Progression?
An Arithmetic Progression is a sequence in which the difference between consecutive terms is constant.
Q2. What is the common difference?
The common difference is the fixed difference between consecutive terms of an AP.
Q3. What is the formula for the nth term of an AP?
The nth term is given by:
$$a_n=a+(n-1)d$$
Q4. What is the formula for the sum of the first n terms?
The formula is:
$$S_n=\frac{n}{2}[2a+(n-1)d]$$
Q5. Can the common difference of an AP be negative?
Yes. For example, in the sequence 20, 17, 14, 11, …, the common difference is:
$$d=17-20$$
$$d=-3$$
Conclusion
Arithmetic Progressions are an important chapter in Class 10 Mathematics. Understanding the first term, common difference, nth term and sum formulas makes it easier to solve both MCQs and descriptive questions.
Related links
- Class 10 Science Chapter 2 Acids, Bases and Salts part-8
- Class 10 History Chapter 2 Nationalism in India part-5
- Class 10 English Chapter 2 Nelson Mandela: Long Walk to Freedom part-6
- Class 10 Maths Chapter 4 Quadratic Equations part-15
- Class 10 Science Chapter 2 Acids, Bases and Salts part-7
- Class 10 History Chapter 2 Nationalism in India part-4
- Class 10 English Chapter 2 Nelson Mandela: Long Walk to Freedom part-5
- Class 10 Maths Chapter 4 Quadratic Equations part-14
- Class 10 History Chapter 2 Nationalism in India part-3
- Class 10 Science Chapter 2 Acids, Bases and Salts part-6
- Class 10 English Chapter 2 Nelson Mandela: Long Walk to Freedom PART-4
Latest Posts
- Class 10 Science Chapter 2 Acids, Bases and Salts
- Class 9 Science Chapter 2 Is Matter Around Us Pure
- Class 7 Science Chapter 2 Nutrition in Animals
- Class 8 Science Chapter 2 Microorganisms Friend and Foe
- Class 8 History Chapter 2 From Trade to Territory
Join Our Other Communities
Instagram , Youtube , Facebook
