This chapter introduces arithmetic progressions (AP), providing insights into their structure and properties. Key concepts include the definition of AP, its common difference, and how to derive the nth term and the sum of the first n terms. Practical examples and exercises illustrate the application of these concepts in various real-life scenarios.
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Sections
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NCERT Study MaterialClass Notes
Memorization
What we have learnt
- An arithmetic progression (...
- The nth term of an AP can b...
- The sum of the first n term...
Final Test
Revision Tests
Chapter FAQs
What we have learnt
- An arithmetic progression (AP) is defined as a list of numbers where each term is obtained by adding a fixed number (common difference) to the preceding term.
- The nth term of an AP can be calculated using the formula: a_n = a + (n - 1)d, where 'a' is the first term and 'd' is the common difference.
- The sum of the first n terms of an AP is given by the formula: S_n = n/2 * (2a + (n - 1)d), or alternatively, S_n = n/2 * (a + l) where 'l' is the last term.
Key Concepts
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Term: Arithmetic Progression (AP)
Definition: A sequence of numbers where the difference between consecutive terms is constant.
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Term: Common Difference (d)
Definition: The fixed number that is added to each term in an AP to obtain the next term.
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Term: nth Term of an AP
Definition: The term at position n in an AP, defined by a_n = a + (n - 1)d.
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Term: Sum of the First n Terms (S_n)
Definition: The total obtained by adding the first n terms of an AP, calculated using S_n = n/2 * (2a + (n - 1)d).