📚 Arithmetic Progressions (AP) Class 10 Notes in Hindi & English | Formula, PYQ, MCQ, Important Questions with Answers
Class 10 Mathematics Chapter 5 – Arithmetic Progressions (AP)
क्या आप Class 10 Maths Chapter Arithmetic Progressions (AP) की पूरी तैयारी करना चाहते हैं? इस पोस्ट में आपको AP की Definition, Formulas, Important Concepts, Previous Year Questions (PYQ), Expected Questions, MCQs, Practice Questions और Exam Tips हिंदी एवं अंग्रेजी दोनों भाषाओं में मिलेंगे।
यह पोस्ट CBSE, ICSE, State Board तथा सभी Class 10 छात्रों के लिए उपयोगी है। Previous topic : Linear Equation In Two Variables.
📑 Table of Contents ( Arithmetic Progressions )
- What is Arithmetic Progression?
- Definition in English & Hindi
- Important Abbreviations
- Key Concepts of AP
- Important Formulas
- Solved Examples
- Previous Year Questions (PYQ)
- Expected Board Exam Questions
- MCQs for Practice
- Important Exam Tips
- Viewer Challenge Questions
🔹 What is Arithmetic Progression (AP)?
English Definition
An Arithmetic Progression (AP) is a sequence of numbers in which the difference between any two consecutive terms remains constant.
Example:
2, 5, 8, 11, 14, …
Here,
5 − 2 = 3
8 − 5 = 3
11 − 8 = 3
The common difference remains 3.
Therefore, this sequence is an Arithmetic Progression.
हिंदी में परिभाषा
अंकगणितीय प्रगति (Arithmetic Progression – AP) ऐसी संख्या श्रेणी होती है जिसमें प्रत्येक दो क्रमागत पदों का अंतर समान रहता है।
उदाहरण:
2, 5, 8, 11, 14, …
यहाँ प्रत्येक पद का अंतर 3 है।
अतः यह एक AP है।
🔹 Important Abbreviations
| Symbol | Meaning |
|---|---|
| AP | Arithmetic Progression |
| a | First Term (प्रथम पद) |
| d | Common Difference (सार्व अंतर) |
| n | Number of Terms |
| Tn | nth Term |
| Sn | Sum of n Terms |
| l | Last Term |
🔹 Key Concepts of Arithmetic Progressions
English
| Every AP has a constant common difference. |
| AP can be Increasing AP. |
| nth term helps us find any term directly. |
| AP can be Decreasing AP. |
| Sum formula helps calculate large sums quickly |
| AP can also be Constant AP. |
हिंदी
| प्रत्येक AP में सार्व अंतर स्थिर होता है। |
| AP बढ़ती हुई हो सकती है। |
| nवाँ पद किसी भी पद को सीधे ज्ञात करने में सहायता करता है। |
| AP घटती हुई भी हो सकती है। |
| योग सूत्र से बड़ी गणनाएँ आसान हो जाती हैं। |
| AP स्थिर भी हो सकती है। |
🔹 Types of Arithmetic Progressions
1. Increasing AP
Example:
3, 6, 9, 12, 15
Common Difference = +3
2. Decreasing AP
Example:
20, 15, 10, 5, 0
Common Difference = -5
3. Constant AP
Example:
7, 7, 7, 7, 7
Common Difference = 0
🔹 Important Formulas for Class 10 AP
Formula 1: Common Difference
d = a₂ − a₁
Example:
10, 15, 20, 25
d = 15 − 10 = 5
Formula 2: nth Term
Tn = a + (n − 1)d
This formula is very important for board exams.
Example:
Find 15th term of AP:
2, 5, 8, 11,…
a = 2
d = 3
n = 15
T15 = 2 + (15 − 1) × 3
= 2 + 42
= 44
✅ Answer = 44
Formula 3: Sum of n Terms
Sn = n/2 [2a + (n − 1)d]
Example:
Find sum of first 10 terms:
2, 5, 8, 11,…
a = 2
d = 3
n = 10
S10 = 10/2 [4 + 27]
= 5 × 31
= 155
✅ Answer = 155
🔹 Solved Example
Question
Find the 20th term of AP:
7, 10, 13, 16,…
Solution
a = 7
d = 3
n = 20
T20 = 7 + (20 − 1) × 3
= 7 + 57
= 64
✅ Answer = 64
🔹 Previous Year Questions (PYQ)
PYQ 1
Find the common difference of:
21, 17, 13, 9,…
Answer:
d = -4
PYQ 2
Find the 18th term of AP:
5, 8, 11, 14,…
Answer:
56
PYQ 3
Find the sum of first 20 terms:
3, 7, 11, 15,…
Answer:
820
PYQ 4
Which term of AP
2, 7, 12, 17,…
is 77?
Answer:
16th Term
🔹 Expected Questions for Board Exams 2026
Q1
Define Arithmetic Progression.
Q2
What is Common Difference?
Q3
Write the formula of nth term.
Q4
Write the formula of sum of n terms.
Q5
Find the 25th term of AP:
4, 9, 14, 19,…
Q6
Find the sum of first 15 terms:
7, 10, 13,…
Q7
Determine whether
5, 10, 15, 20,…
is an AP or not.
🔹 MCQs for Practice
1. The common difference of AP
4, 8, 12, 16
is:
A) 2
B) 3
C) 4
D) 5
✅ Answer: C
2. First term of AP
9, 13, 17, 21
is:
A) 9
B) 13
C) 17
D) 21
✅ Answer: A
3. nth term formula is:
A) a+d
B) a×d
C) a+(n−1)d
D) nd
✅ Answer: C
4. Which of the following is an AP?
A) 2,4,8,16
B) 1,3,5,7
C) 2,6,18,54
D) 1,4,9,16
✅ Answer: B
5. Common difference of
25, 20, 15, 10
is:
A) 5
B) -5
C) 10
D) -10
✅ Answer: B
🎯 Viewer Challenge – Solve & Get Featured
अपनी कॉपी में हल करें और Answer Comment या Message करें।
Question 1
Find the 15th term of AP:
4, 9, 14, 19,…
Question 2
Find the Common Difference:
35, 30, 25, 20,…
Question 3
Find the Sum of First 12 Terms:
2, 5, 8, 11,…
Question 4
Which term of AP
7, 12, 17, 22,…
is 102?
Question 5
Find the 25th term of AP:
3, 7, 11, 15,…
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💡 Important Exam Tips
| NCERT Examples को अच्छी तरह पढ़ें। |
| Exercise 5.1, 5.2 और 5.3 बार-बार हल क |
| Formula याद करने के साथ-साथ उनका उपयोग भी समझें। |
| PYQ Questions अवश्य हल करें। |
| Board Exam में AP Chapter से लगभग हर वर्ष प्रश्न पूछे जाते हैं। |
| Case Study एवं Competency Based Questions की भी तैयारी करें। |
📚 Class 10 Maths Preparation Series
Chapter: Arithmetic Progressions (AP)
Topic Covered: Definition, Formula, PYQ, MCQ, Important Questions, Board Exam Preparation, Hindi & English Notes
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