ഒരുപാട് ആവർത്തിച്ച ചോദ്യങ്ങൾ | ARITHMETIC PROGRESSION | സമാന്തരശ്രേണി | PART-2 | PSC | SSC | RRB |

Introduction

This tutorial focuses on understanding Arithmetic Progression (AP), specifically aimed at enhancing your preparation for competitive exams like PSC, SSC, and RRB. The concepts covered in this guide will help you grasp AP more effectively, especially if you have encountered repeated questions on this topic.

Step 1: Understanding the Basics of Arithmetic Progression

• Definition: An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the "common difference" (d).
• General Form: The nth term of an AP can be expressed as:
  • ( a_n = a + (n - 1)d )
  • Where:
    • ( a_n ) = nth term
    • ( a ) = first term
    • ( n ) = number of terms
    • ( d ) = common difference

Practical Tips

• Familiarize yourself with identifying the first term and common difference in given sequences.
• Practice deriving the nth term formula with different values.

Step 2: Calculating the Sum of an Arithmetic Progression

• Formula for the Sum: The sum of the first n terms (S_n) of an AP can be calculated using:
  • ( S_n = \frac{n}{2} \times (2a + (n - 1)d) )
  • Alternatively:
  • ( S_n = \frac{n}{2} \times (a + a_n) )
  • Where:
    • ( S_n ) = sum of the first n terms
    • ( n ) = number of terms
    • ( a_n ) = nth term

Common Pitfalls to Avoid

• Ensure you correctly identify the first term and the common difference before applying the formulas.
• Double-check your calculations, especially when dealing with larger numbers.

Step 3: Solving Common Problems in Arithmetic Progression

• Finding the nth term:

  1. Identify the first term (a) and common difference (d).
  2. Use the nth term formula to calculate.

• Calculating the sum of terms:

  1. Determine the number of terms (n).
  2. Apply the sum formula based on either the first term and common difference or the first and last term.

Example Problem

• Given the first term ( a = 3 ) and common difference ( d = 2 ), find the 10th term and the sum of the first 10 terms.
  • 10th term:
    • ( a_{10} = 3 + (10 - 1) \times 2 = 3 + 18 = 21 )
  • Sum of the first 10 terms:
    • ( S_{10} = \frac{10}{2} \times (2 \times 3 + (10 - 1) \times 2) = 5 \times (6 + 18) = 5 \times 24 = 120 )

Conclusion

Understanding arithmetic progression is essential for excelling in competitive exams. Remember the key formulas for the nth term and the sum of the terms, and practice solving various problems to reinforce your understanding. As you prepare, consider joining study groups or channels focused on competitive exam preparation for further insights and practice questions.