Arithmetic Progressions

Board: CBSE Class: 10

Chapter Overview

An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number d (common difference) to the preceding term. The nth term of an AP is a_n = a + (n-1)d, where a is the first term. The sum of the first n terms is S_n = n/2[2a + (n-1)d] = n/2(a + l), where l is the last term. Word problems involve patterns, installment schemes, and real-life situations.

Topics Covered

AP Definition
Common Difference
nth Term of AP
Sum of n Terms
Sum Using Last Term
AP Word Problems
Finding Number of Terms

Key Formulas

a_n = a + (n-1)d

S_n = n/2[2a + (n-1)d]

S_n = n/2(a + l)

d = a_n - a_(n-1)

Real-World Applications

Applications: Loan amortization, savings plans, ticket pricing patterns, natural number sums.

Study Tips

Tip: Identify first term and common difference carefully

Tip: Practice sum formulas with both forms

Tip: Solve NCERT word problems thoroughly