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.