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Key examples such as salary increments, ladder rungs, and other common sequences illustrate the concept of arithmetic progressions. The section defines AP as a sequence where each term is generated by adding a constant value (common difference) to the previous term, setting the foundation for further study in the chapter.
This section focuses on the concept of Arithmetic Progressions (AP), emphasizing the occurrence of patterns in various aspects of nature and daily life. The text begins by presenting real-world examples that illustrate sequences where successive terms are obtained by adding a constant number to the preceding term, known as the common difference.
The section clearly states that an arithmetic progression is defined as a sequence where each term after the first is obtained by adding a fixed number (the common difference) to the previous term. Additionally, it mentions finite and infinite APs, detailing the need for both the first term (denoted as 'a') and the common difference (denoted as 'd') to establish the progression.
Arithmetic Progression (AP): A sequence where each term is generated by adding a constant to the preceding term.
Common Difference: The fixed number added to find the next term in an AP.
Finite AP: An AP with a limited number of terms.
Infinite AP: An AP with no fixed last term.
Terms in a line, add d with ease, with each step, your result will please.
Once a rabbit named Reena calculated her path towards her job, figuring her monthly pay as she went through the years - that was her magical arithmetic progression.
Terms in AP = 'A Simple Definition' for AP: Add, Sequence, Previous.
Reena's salary increments form an arithmetic progression.
Ladder rungs with decreasing lengths represent an arithmetic progression.
Savings that increase by a constant amount over time form an arithmetic sequence.
Term: Arithmetic Progression (AP)
Definition: A sequence of numbers in which the difference between consecutive terms is constant.
A sequence of numbers in which the difference between consecutive terms is constant.
Term: Common Difference (d)
Definition: The fixed amount added to each term of an arithmetic progression to obtain the next term.
The fixed amount added to each term of an arithmetic progression to obtain the next term.
Term: Finite AP
Definition: An arithmetic progression that has a specific number of terms.
An arithmetic progression that has a specific number of terms.
Term: Infinite AP
Definition: An arithmetic progression that continues indefinitely without a final term.
An arithmetic progression that continues indefinitely without a final term.