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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
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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.
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