Mathematics · Class 10
Arithmetic Progressions
nth term, sum of n terms, and AP applications.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
An Arithmetic Progression (AP) has a constant difference d between consecutive terms. Class 10 focuses on nth term and sum of n terms — frequent board questions.
Formulas
nth term
aₙ = a + (n−1)d
Sum of n terms
Sₙ = n/2 [2a + (n−1)d] = n/2 (a + l)
Common difference
d = aₙ − aₙ₋₁
Properties
- If a, b, c are in AP then 2b = a + c
- d can be positive, negative, or zero
- Graph of aₙ vs n is a straight line
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Find 10th term
AP: 3, 7, 11, ... Find a₁₀.
- 1a = 3, d = 4
- 2a₁₀ = 3 + 9×4 = 39
Answer
39
Example 2: Sum
Find sum of first 20 terms of AP with a = 5, d = 3.
- 1S₂₀ = 20/2 [2×5 + 19×3]
- 2= 10 [10 + 57] = 670
Answer
670
Key Points to Remember
- ✓ Identify a and d from the sequence
- ✓ Word problems: form AP from context
- ✓ Check if n is a natural number
Exam Tips
- • State formula before substituting
- • For word problems, define variables first
Practice MCQs — Arithmetic Progressions
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Common difference of 5, 8, 11, ...: