Access the official NCERT Class 10 Mathematics textbook for Chapter 5 – Arithmetic Progressions PDF. This chapter introduces the concept of arithmetic sequences, where each term differs from the previous one by a constant called the common difference (d). You’ll learn to find the nth term using an=a+(n−1)d, derive the sum of n terms Sn=n2[2a+(n−1)d], and apply these concepts in real-world problems like calculating total distances, savings, or production outputs.
Chapter Highlights:
- Definition of Arithmetic Progression (AP): first term (a) & common difference (d)
- General form: a, a+d, a+2d, a+3d, \dots
- Finding the n^\text{th} term: a_n = a + (n-1)d
- Sum of first n terms: S_n = \frac{n}{2}[2a + (n-1)d] or \frac{n}{2}(a + a_n)
- Types of APs: finite vs infinite
- Reverse nth term formula: a_{n-k+1} = a + (n-k)d
- Practical problems: real-life use cases like monthly savings, staircase steps, etc.