Mastering Arithmetic Progression (AP) is crucial for Class 10 students aiming for excellence in the CBSE board exams. This chapter not only lays the foundation for higher mathematical concepts but also carries significant weightage in the examination.
Our comprehensive guide provides detailed NCERT exemplar solutions, marking schemes, expert tips, and curated video tutorials to enhance your understanding and performance.
Table of Contents
- Introduction to Arithmetic Progression
- NCERT Exemplar Solutions: Step-by-Step Guide
- Marking Scheme and Tips to Score Full Marks
- Video Tutorials for Better Understanding
- FAQs on Arithmetic Progression
Introduction to Arithmetic Progression
An Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is known as the common difference (d). The general form of an AP is:
a, a + d, a + 2d, a + 3d, ...
- a = First term
- d = Common difference
- nth term (Tn) = a + (n - 1)d
- Sum of n terms (Sn) = n/2 [2a + (n - 1)d]
Understanding these formulas is essential for solving problems related to AP. For a comprehensive list of formulas, refer to our Class 10 Maths All Formulas Chapterwise.
NCERT Exemplar Solutions: Step-by-Step Guide
Example 1:
Problem: Find the 10th term of the AP: 2, 7, 12, 17, ...
- First term (a) = 2
- Common difference (d) = 7 - 2 = 5
- n = 10
- Tn = a + (n - 1)d = 2 + (10 - 1)×5 = 2 + 45 = 47
Answer: 47
Example 2:
Problem: Which term of the AP: 3, 8, 13, 18, ... is 78?
- First term (a) = 3
- Common difference (d) = 5
- Let Tn = 78
- 78 = 3 + (n - 1)×5
- 75 = 5(n - 1) → n = 16
Answer: 16th term
For more detailed solutions, visit our Class 10 Maths NCERT Exemplar Solutions.
Marking Scheme and Tips to Score Full Marks
- 1 Mark: Direct formula use
- 2 Marks: Specific term/sum finding
- 3 Marks: Application-based logic
- 4 Marks: Long questions with derivation
Full Marks Tips:
- Memorize formulas
- Practice regularly
- Revise weak concepts
- Time yourself during practice
For chapter weightage, visit: Class 10 Maths Chapter-wise Weightage
Video Tutorials for Better Understanding
Understanding Arithmetic Progression
NCERT Exemplar Problems on AP
Tips and Tricks for Solving AP Problems
FAQs on Arithmetic Progression
Q1: What is the formula to find the nth term of an AP?
Answer: Tn = a + (n - 1)d
Q2: How do I find the sum of the first n terms of an AP?
Answer: Sn = n/2 [2a + (n - 1)d]
Q3: What is the common difference in an AP?
Answer: It is the fixed difference between any two consecutive terms.
Q4: Can the common difference be negative?
Answer: Yes, in decreasing sequences.
Q5: Where can I find more practice questions on AP?
Answer: Visit: Class 10 Maths NCERT Exemplar Solutions