Vedantu’s RD Sharma Solutions Chapter 9 - Arithmetic Progressions (Ex 9.2) Free PDF
FAQs on RD Sharma Class 10 Solutions Chapter 9 - Exercise 9.2
1. What is the fundamental formula used to solve most questions in RD Sharma Class 10 Maths Chapter 9, Exercise 9.2?
The primary formula for Exercise 9.2 is the formula for the nth term of an Arithmetic Progression (AP). It is given by: an = a + (n-1)d, where 'a' is the first term, 'd' is the common difference, and 'an' is the nth term of the sequence. Mastering this formula is key to solving the problems.
2. How do you find the common difference (d) of an AP if two non-consecutive terms are given, a common problem type in Exercise 9.2?
To find the common difference (d) when given two terms, say the pth term (ap) and the qth term (aq), you should follow these steps:
- Set up two equations using the nth term formula: ap = a + (p-1)d and aq = a + (q-1)d.
- Subtract one equation from the other to eliminate the first term 'a'. This will leave you with an equation solely in terms of 'd'.
- Solve the resulting equation to find the value of the common difference (d).
3. Why is correctly identifying the 'first term (a)' and 'common difference (d)' the most critical first step for any problem in this exercise?
Identifying 'a' and 'd' is crucial because they are the two fundamental building blocks that define a unique Arithmetic Progression. Every other value in the sequence, including any specific term (an) or the sum of terms (Sn), is derived from them. An incorrect 'a' or 'd' will lead to a completely wrong sequence and incorrect answers for all subsequent parts of the problem.
4. Can the common difference (d) in an AP be a fraction or a negative number? How does this apply to problems in Exercise 9.2?
Yes, the common difference (d) can be any real number—positive, negative, zero, or a fraction.
- A positive 'd' results in an increasing AP (e.g., 2, 5, 8,...).
- A negative 'd' results in a decreasing AP (e.g., 10, 8, 6,...).
- A fractional 'd' results in terms that are not whole numbers (e.g., 1, 1.5, 2,...).
5. How do I solve problems in Exercise 9.2 that ask to find which term of a given AP is a specific value (e.g., which term is 0)?
To solve such problems, you need to use the nth term formula, an = a + (n-1)d. Here is the step-by-step method:
- Identify the first term (a) and common difference (d) from the given AP.
- Set the value of the term you are looking for as an (e.g., set an = 0).
- Substitute the known values of a, d, and an into the formula.
- The only unknown variable remaining will be 'n'. Solve the linear equation for 'n' to find the position of the term.
6. What is a common mistake to avoid when checking if a particular number is a term in a given AP?
A very common mistake is not verifying the nature of the result for 'n'. When you use the formula an = a + (n-1)d to solve for 'n', the value of 'n' must be a positive integer. A term's position cannot be a fraction, a negative number, or zero. If your calculation for 'n' results in anything other than a positive integer, it proves that the given number is not a term in that specific AP.
7. Are the RD Sharma Solutions for Exercise 9.2 sufficient for CBSE board exam preparation?
Yes, the solutions for RD Sharma Exercise 9.2 offer extensive practice on the concept of the nth term of an AP. The variety and complexity of problems are generally higher than in the NCERT textbook, which helps build a strong conceptual foundation and problem-solving speed. This is highly beneficial for the CBSE Class 10 board exams for 2025-26.
