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8.Arithmetic Progression (AP)
Class 11 • Mathematics • NCERT
Arithmetic Progression (AP)
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This lesson introduces Arithmetic Progressions as per NCERT Class 11. Students learn the definition of an AP, identify the first term and common difference, and find the general term of an AP using simple, exam-oriented examples.
Lesson Objectives
- Understand what an Arithmetic Progression is.
- Identify the first term and common difference.
- Find the nth term of an AP.
- Solve basic NCERT-style problems.
1. What Is an Arithmetic Progression?
An Arithmetic Progression (AP) is a sequence in which the difference between any two consecutive terms is constant.
Examples of APs:
• 2, 4, 6, 8, …
• 5, 10, 15, 20, …
• 2, 4, 6, 8, …
• 5, 10, 15, 20, …
2. First Term and Common Difference
In an AP:
• First term = a
• Common difference = d = second term − first term
• Common difference = d = second term − first term
3. General Term of an AP
The nth term (general term) of an AP is given by:
Tn = a + (n − 1)d
4. Simple NCERT Examples
• Find the 5th term of AP: 2, 4, 6, …
Here, a = 2, d = 2
T5 = 2 + (5 − 1)×2 = 10
Here, a = 2, d = 2
T5 = 2 + (5 − 1)×2 = 10
5. Important NCERT Notes
• AP can have positive, negative, or zero common difference
• Sequence with d = 0 is a constant AP
• n represents the position of the term
• Sequence with d = 0 is a constant AP
• n represents the position of the term
Practice Questions (NCERT)
- Define an Arithmetic Progression.
- Find the common difference of AP: 3, 7, 11, …
- Write the first term of AP: 5, 9, 13, …
- Write the formula for the nth term of an AP.
- Find the 6th term of AP: 2, 5, 8, …
- Can the common difference be negative?
- What happens if d = 0?
- What does n represent in Tn?
- Is 1, 1, 1, … an AP?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- A sequence with constant difference between consecutive terms.
- 4
- 5
- Tn = a + (n − 1)d
- 17
- Yes
- AP becomes constant.
- Position of the term.
- Yes
- Yes
© Aviate Learning – Sequences & Series (NCERT Class 11)