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Arithmetic Progression

This chapter introduces Arithmetic Progression (AP), an important concept in Class 10 Mathematics. An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference. In this chapter, students learn how to identify arithmetic progressions, find terms of the sequence, and calculate the sum of a given number of terms. These concepts are widely used in algebra and real-life problem solving. Topics covered in this chapter: β€’ Introduction to Arithmetic Progression β€’ First term and common difference β€’ Finding the nα΅—Κ° term of an AP β€’ Sum of first n terms of an AP β€’ Solving problems based on arithmetic sequences

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This PDF includes: Introduction to AP General form First term & common difference Types of AP 𝑛 𝑑 β„Ž n th term formula Number of terms formula Sum of 𝑛 n terms formulas Important properties Applications of AP Important series formulas.

Formula Bank

Common Difference
d=anβ€‹βˆ’anβˆ’1
nth Term Formula
an​=a+(nβˆ’1)d
Finding Number of Terms
n=\frac{\left(an-a\right)}{d}+1
Sum of First n Terms
Sn=\frac{n}{2}[2a+(n-1)d]
Alternative Sum Formula
Sn​=2n​(a+l)
Last Term Formula
𝑙 = π‘Ž + ( 𝑛 βˆ’ 1 ) 𝑑
Property of AP For three numbers in AP:
2 𝑏 = π‘Ž + 𝑐
Sum of first n even numbers
𝑆 𝑛 = 𝑛 ( 𝑛 + 1 )
Sum of first n odd numbers
Sn=n^2

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