Wrong shortcode initialized

I. Chapter Summary

This chapter introduces the concept of Arithmetic Progressions (AP)—a sequence of numbers in which the difference between any two consecutive terms is constant. It explains how to identify an AP, find the nth term, and calculate the sum of the first n terms. These concepts are applicable in both academic and real-world contexts such as budgeting, project planning, and salary computations.

II. Key Concepts Covered

Concept	Explanation
Arithmetic Progression (AP)	A sequence where the difference between consecutive terms is constant, called the common difference (d).
General Term (nth term)
Formula: $a_n = a + (n – 1)d$,
Where:
• a = first term,
• d = common difference,
• n = number of terms
Sum of First n Terms (Sₙ)
Formula 1: $S_n = frac{n}{2} left[ 2a + (n – 1)d right]$
Formula 2: $S_n = frac{n}{2}(a + l)$ where l is the last term
Finding number of terms	Rearranging the nth term or sum formula based on known values
Real-life Applications	Used in schedules, salary increments, installment payments, etc.

III. Important Questions

(A) Multiple Choice Questions (1 Mark)

1. Which of the following sequences is an AP?
   a) 2, 4, 8, 16
   b) 3, 6, 9, 12 ✅ (PYQ 2021)
   c) 1, 3, 6, 10
   d) 10, 7, 3, -1
2. If the first term of an AP is 5 and the common difference is 3, what is the 10th term?
   a) 32
   b) 35 ✅
   c) 30
   d) 33
3. If $a = 7, d = 0$, then the AP is:
   a) Constant sequence ✅
   b) Geometric
   c) Not defined
   d) Increasing
4. What is the sum of first 5 terms of the AP: 2, 4, 6, …?
   a) 20
   b) 25 ✅
   c) 30
   d) 28

(B) Short Answer Questions (2/3 Marks)

1. Find the 12th term of the AP: 7, 10, 13, 16, … (PYQ 2019)
2. Which term of the AP: 3, 8, 13, 18, … is 88?
3. How many terms of the AP: 9, 17, 25, … must be taken to get the sum 636?
4. Find the sum of first 15 terms of the AP whose first term is 5 and the common difference is 3.

(C) Long Answer Questions (5 Marks)

1. The sum of the 4th and 8th terms of an AP is 24. If the 10th term is 41, find the AP.
2. If the sum of the first n terms of an AP is 5n² + 3n, find the first term and the 20th term.
3. A sum of ₹700 is to be used to give 7 cash prizes to students. Each prize is ₹20 more than the previous one. Find the value of each prize.
4. The houses of a row are numbered consecutively from 1 to 49. Show that the sum of the numbers is 1225 using AP formula.

(D) HOTS (Higher Order Thinking Skills)

1. If the 5th term of an AP is 0 and the 9th term is 16, find the AP and the sum of its first 10 terms.
2. A man saves ₹30 in the first month, ₹40 in the second, ₹50 in the third, and so on for 12 months. How much does he save in a year?

IV. Key Formulas/Concepts

Formula	Use
$a_n = a + (n – 1)d$	To find the nth term
$S_n = frac{n}{2} left[ 2a + (n – 1)d right]$	To find the sum of n terms
$S_n = frac{n}{2}(a + l)$	When last term is known
$d = a_2 – a_1$	To find common difference
For word problems	Define terms using variables and apply formulas systematically

V. Deleted Portions (CBSE 2025–2026)

 No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026)

Unit/Chapter	Estimated Marks	Types of Questions Typically Asked
Chapter 5: Arithmetic Progressions	6–8 Marks	1 Long Answer, 2 Short Answers, 1 MCQ

VII. Previous Year Questions (PYQs)

Year	Marks	Question
2021	1	Identify AP: 3, 6, 9, 12 ✅
2020	3	Find the term which is 88 in the AP: 3, 8, 13…
2019	2	Find the 12th term of 7, 10, 13…
2018	5	Total prize distribution problem with AP logic

VIII. Real-World Application Examples

Situation	Application
Salary Increments	Annual raises form an AP
Installments	EMIs and reducing balances often follow AP logic
Ladder Steps, Seating Arrangements	Equal gaps form APs
Savings Plans	Monthly increase in deposits modelled using AP

IX. Student Tips & Strategies for Success

Time Management

• Dedicate 15 minutes daily to AP practice.
• Use a formula sheet for quick revision.

Exam Preparation

• Focus on distinguishing between “term position” and “term value.”
• Practice word problems (scholarships, savings, prizes).

Stress Management

• Use examples from real life to relate and visualize APs.
• Build confidence by solving small 5-question sets.

X. Career Guidance & Exploration (Class-Specific)

For Classes 9–10

Streams

• Science: Physics, Engineering
• Commerce: Business Math, Finance
• Arts: Logical Reasoning, Civil Planning

Career Paths

• Data Analyst, Civil Engineer, Investment Banker

Competitive Exams

• NTSE, CUET Quant, RMO, Olympiads

XI. Important Notes

• Visit https://ncert.nic.in and https://cbseacademic.nic.in for updates.
• Understand real-world relevance of APs to enhance memory.
• Consistent formula practice ensures long-term retention and confidence.