Arithmetic Progressions

For the 2025–2026 academic year, the most important topics in Class 10 Maths for Arithmetic Progressions (AP) include the general form of an AP, the formula for the

nthn raised to the t h power𝑛𝑡ℎ term, and the formula for the sum of the first

nn𝑛 terms. The key focus is on applying these formulas to solve various problems, including daily life situations. 

Key topics in arithmetic progressions 

Definition of an AP 

• Identification of an AP: Students should be able to determine if a given list of numbers forms an AP by checking if the common difference (dd𝑑) between consecutive terms is constant.
• General form: Understand the general representation of an AP as: a,a+d,a+2d,a+3d,…a comma a plus d comma a plus 2 d comma a plus 3 d comma point point point𝑎,𝑎+𝑑,𝑎+2𝑑,𝑎+3𝑑,…, where aa𝑎 is the first term and dd𝑑 is the common difference. 

nthn raised to the t h power𝑛𝑡ℎ term of an AP 

• Formula: Master the formula for the nthn raised to the t h power𝑛𝑡ℎ term of an AP, given by an=a+(n−1)da sub n equals a plus open paren n minus 1 close paren d𝑎𝑛=𝑎+(𝑛−1)𝑑.
• Applications: Practice problems involving finding a specific term of an AP, finding the number of terms in a finite AP, or determining if a given number is a term of a specific AP.
• Problem-solving: Solve questions where you must find the first term (aa𝑎) and the common difference (dd𝑑) using given information about different terms of the AP. 

Sum of the first

nn𝑛 terms of an AP 

• Formulas: Learn both formulas for the sum of the first nn𝑛 terms (Sncap S sub n𝑆𝑛):
  • Sn=n2[2a+(n−1)d]cap S sub n equals n over 2 end-fraction open bracket 2 a plus open paren n minus 1 close paren d close bracket𝑆𝑛=𝑛2[2𝑎+(𝑛−1)𝑑] (when the first term and common difference are known)
  • Sn=n2(a+l)cap S sub n equals n over 2 end-fraction open paren a plus l close paren𝑆𝑛=𝑛2(𝑎+𝑙) (when the first and last terms are known)
• Applications: Solve problems related to finding the sum of a specific number of terms and finding the number of terms when the sum is given. 

Word problems 

• Real-life scenarios: A major focus of the chapter is the application of AP concepts to daily life problems. Expect questions based on common themes, including:
  • Savings and installments: Problems where a fixed amount is saved or paid each month.
  • Construction: Problems involving sequences like logs stacked in piles or steps of a ladder.
  • General progressive patterns: Finding the total output over time if there is a fixed increase or decrease each period.
• Complex word problems: Practice multi-step problems where you may need to form and solve linear equations to find the required AP values