Arithmetic Progressions

• Definition and Introduction

  • An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
  • General form: a, a + d, a + 2d, a + 3d, ...
  • Where 'a' is the first term and 'd' is the common difference.

• Types of Arithmetic Progressions

  • Finite AP: Has a fixed number of terms
  • Infinite AP: Has an infinite number of terms

• Key Formulae

  • nth term: an = a + (n - 1)d
  • Sum of AP: Sn = n/2 [2a + (n - 1)d]

• Mean and Median of A.P.

  • Mean: (first term + last term) / 2
  • Median: (n + 1)th term

• Examples and Applications

  • Finding the sum of the first n terms of an AP
  • Finding the nth term of an AP
  • Real-life applications: finance, geometry, etc.

• Solved Examples

  • Example 1: Find the 10th term of an AP with first term 5 and common difference 3
  • Example 2: Find the sum of the first 15 terms of an AP with first term 10 and common difference -2

• Practice Questions

  • Find the 20th term of an AP with first term 8 and common difference 2
  • Find the sum of the first 25 terms of an AP with first term 15 and common difference -1