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Welcome to one of the most scoring and logically fascinating topics in your CBSE Class 10 Mathematics syllabus: Arithmetic Progressions. When you look at a sequence of numbers that increases or decreases by a fixed amount—like the rungs of a ladder, the seating rows in a stadium, or a savings account growing by a constant amount each month—you are observing an Arithmetic Progression (AP). But what if you need to find the value of the 50th or 100th step without writing out the entire sequence one by one? This is where the concept of the nth term of an AP becomes incredibly useful, allowing you to instantly calculate any specific term in a sequence using a simple, unified rule.
The core logic of finding the nth term relies on understanding how the sequence is fundamentally built. Every single term is generated by adding a fixed number, called the common difference (d), to the previous term. Starting from the first term (a), the second term is a + d, the third term is a + 2d, and so on. Notice the distinct pattern: the number of times you add d is always exactly one less than the position of the term itself. Therefore, the general formula for the nth term (often denoted as an) is mathematically expressed as: an = a + (n - 1)d. Here, n represents the position or term number you want to find. By simply plugging in these three known variables, you can bypass tedious manual addition and jump directly to your answer.
Take a look at the diagram above, which clearly visualizes an Arithmetic Progression where the sequence begins with 3 and grows by 4 at each step. As shown by the green circles, the first term (a) is 3. To reach the second term, we add the common difference (d = 4) once, arriving at 7. To reach the third term, we add d twice, giving us 11, and the mathematical pattern continues perfectly. The diagram vividly illustrates the core rule: to find the value of any term, you add the common difference exactly one less time than the term's position. The bottom section of the graphic applies this logic to find the 10th term (a10) by substituting a = 3, n = 10, and d = 4 into the formula, yielding a final answer of 39. In your CBSE board exams, questions will frequently ask you to find a specific term like this, determine the total number of terms in a finite AP, or identify which exact position holds a particular value (e.g., "Which term of the AP is 78?"). Mastering this formula is the absolute key to solving these word problems accurately.
Grasping the concept of the nth term of an AP is a fundamental stepping stone to mastering the entire Arithmetic Progressions chapter. If you find yourself getting confused with sequence formulas, dealing with negative common differences, or breaking down complex word problems, personalized guidance can make a world of difference. On UrbanPro, you can easily find highly experienced, verified Class 10 Mathematics tutors tailored exactly to your learning style. Whether you are looking for interactive online classes or prefer focused local offline tuition near your home, UrbanPro connects you with top-rated educators who can simplify these concepts, provide targeted practice, and ensure you are fully confident and prepared for your board exams.
Other Concepts in Arithmetic Progression
- EXERCISE 5.1
- EXERCISE 5.2
- EXERCISE 5.3
- EXERCISE 5.4
- EXERCISE 5.4 (Optional)*
- Sum of first n terms of an AP
Other Concept Videos for nth term of an AP
Finding the nth Term in an AP
CBSE - Class 10>Mathematics>Arithmetic Progression>nth term of an AP
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Top Tutor 
Munirka, Delhi 
1 student 
48 hrs of classes completed 
200 per hour 
Online Classes I am a teacher since last 3-4 years. I have teaching tuition to students of class 9th and 10th CBSE board. In these covid times i prefer online classes and my subjects of expertise are science, maths ans social science.
Super Tutor Sector 5, Gurgaon 28 students 2162 hrs of classes completed 450 per hour Online Classes 
Tutor's home Mathematics is not just a subject—it is the backbone of science and the foundation for logical thinking and problem-solving. With over eleven years of teaching experience and a B.Tech degree, I am dedicated to nurturing students' mathematical abilities while instilling confidence and a love for learning. Recognitions & Achievements ✅ UrbanPro Excellency Awards – Top 10 in Class 10 Tuition (2024) & Top 100 Tutors for 2024 ✅ Teacher Innovation Award by ZIIEI (Sri Aurobindo Society) ✅ Certified by Leading Ed-Tech Platforms – UrbanPro Certification, GuruQ Certification These accolades reflect my commitment to providing high-quality education and delivering exceptional learning outcomes for my students. Why Choose Me as Your Child’s Tutor? As an educator, my primary goal is to empower students with a strong conceptual foundation while ensuring they enjoy the learning process. I believe that every child has unique strengths and learning needs, and my approach is tailored to bring out the best in them. 📌 Comprehensive Academic Support: I provide in-depth coaching in Mathematics, Science, and English for Grades V–X and specialize in Mathematics for Grades XI–XII and Undergraduate Courses. 📌 Expert in Competitive & Entrance Exam Preparation: I have successfully guided students in securing admissions to prestigious institutions and excelling in competitive exams, including: 🎯 School Entrance Exams – Sainik School, Military School, Navodaya Vidyalaya, Gurukul Entrance, Central Hindu School, Rai Sports School 🎯 Competitive & Government Job Exams – Olympiads, RIMC, NTSE, SSC MTS, CHSL, DSSSB 📌 Proven Track Record of Student Success: My students have consistently demonstrated remarkable improvement in grades and conceptual understanding. I maintain an individualized learning plan for each student, ensuring they receive personalized guidance and continuous support. Regular assessments, progress reports, and feedback sessions help track improvement and address learning gaps effectively. My Teaching Methodology & Approach I strongly believe that learning should be an engaging and interactive experience rather than rote memorization. My experiential learning approach is designed to: ✔ Encourage critical thinking and problem-solving skills ✔ Foster conceptual clarity through real-life applications ✔ Enhance creativity and independent learning To achieve this, I incorporate modern teaching tools and methodologies, such as: 🖥 Live Interactive Sessions – Engaging discussions to clarify doubts in real time 📊 PowerPoint Presentations & Animations – To visualize complex concepts easily 🖋 Whiteboard Teaching – Step-by-step breakdown of mathematical problems 📚 Comprehensive Study Materials, Worksheets & Assignments – Reinforcing learning through practice Online & Offline Classes: I conduct online classes via digital platforms and in-person sessions at my institute in Gurgaon. For students requiring additional support, I offer home tuition when feasible. Commitment to Student Success 🌟 Personalized Attention: I ensure that every student gets the individual focus they need to overcome challenges and master concepts. 🌟 Supportive Learning Environment: My classes are structured to be patient, encouraging, and motivating, allowing students to ask questions freely and develop confidence in their abilities. 🌟 Building Lifelong Skills: Beyond academics, I emphasize the development of problem-solving abilities, logical reasoning, and exam strategies that benefit students in their future careers. 🌟 Parental Involvement & Regular Feedback: I believe in open communication with parents to discuss their child’s progress, strengths, and areas for improvement. Regular performance reviews ensure that parents stay informed about their child's academic growth. Invest in Your Child’s Future Today! With a proven track record, structured teaching approach, and a passion for education, I am committed to helping students achieve excellence in Mathematics and beyond. If you are looking for a dedicated, award-winning tutor who can provide high-quality education, personalized guidance, and measurable results, I would be delighted to support your child’s learning journey. 📩 Contact me today to discuss how I can help your child excel!
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Top Tutor Sector 19, Noida 12 students 584 hrs of classes completed Online Classes • 3+ years of teaching experience. • teaching online tuitions of Mathematics for Class 10-12th. • pursued M.Sc. Mathematics from University of Delhi & B.Sc. Mathematical Sciences from University of Delhi. Passionate about solving mathematical problems and I have helped many students to overcome the fear of Maths.
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FAQ
What is the meaning of nth term of an AP?
It refers to a specific mathematical method or property in Arithmetic Progression used to solve problems involving nth term of an AP.
Why is nth term of an AP important for CBSE - Class 10 exams?
This concept is crucial for the exams as questions related to Arithmetic Progression and specifically nth term of an AP are very common. It helps secure marks in the section effectively.
Is nth term of an AP part of the latest NCERT syllabus?
Yes, nth term of an AP is an integral part of the CBSE - Class 10 NCERT Mathematics syllabus. It is a key topic covered in the Arithmetic Progression chapter.
What are common mistakes students make with nth term of an AP?
Students often miss the minute details or fundamental definitions of nth term of an AP. Regular revision and practice are needed to master the nuances.
How should I approach learning nth term of an AP?
Start by understanding the formulas and logic, then practice applying them to simple problems. Solve the examples given in the NCERT textbook before moving to exercise problems.
How can UrbanPro help me understand nth term of an AP better?
UrbanPro connects you with experienced Mathematics tutors who can explain nth term of an AP with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.
