DownloadMaharashtra Board Class 10 Maths 1 Chapter 3 Solutions explain Arithmetic Progression through patterns, formulas and applications. This page contains clear step-by-step solutions for Practice Sets 3.1 to 3.4 and Problem Set 3.
The solutions follow the Maharashtra State Board Balbharati textbook order. Every substitution and calculation is shown clearly so that students can understand the method and prepare for the SSC examination.
Chapter 3 Arithmetic Progression Overview
An arithmetic progression is a sequence in which the difference between consecutive terms remains constant. Students learn how to identify an arithmetic progression, find a required term and calculate the sum of a given number of terms.
Topics Covered
- Recognising an arithmetic progression
- First term and common difference
- General or nth term
- Finding missing terms
- Finding the number of terms
- Sum of the first n terms
- Applications of arithmetic progression
Important Formulas for Arithmetic Progression
- Common difference: d = t₂ − t₁
- nth term: tₙ = a + (n − 1)d
- Last term: l = a + (n − 1)d
- Sum: Sₙ = n/2 [2a + (n − 1)d]
- When the last term is known: Sₙ = n/2(a + l)
Common Mistakes in Arithmetic Progression
- Using n instead of n − 1 in the nth-term formula.
- Confusing tₙ with Sₙ.
- Assuming that the common difference must be positive.
- Substituting the last term in place of the number of terms.
- Forgetting the correct unit in an application problem.
Frequently Asked Questions about Arithmetic Progression
How do we identify an arithmetic progression?
Find the difference between consecutive terms. The sequence is an arithmetic progression when the difference remains constant.
What is the nth-term formula?
The nth term is tₙ = a + (n − 1)d, where a is the first term and d is the common difference.
What is the difference between tₙ and Sₙ?
tₙ represents one specified term, whereas Sₙ represents the sum of the first n terms.
Can an arithmetic progression decrease?
Yes. An arithmetic progression decreases when its common difference is negative.
