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Sequence and Series

• The Concept of Arithmetic Progression
• An arithmetic progression is a list of numbers in which the difference between any two consecutive terms is equal.
• In an AP, each term, except the first term, is obtained by adding a fixed number called common difference to the preceding term.
• The common difference of an AP can be positive, negative or zero.

Example 1:

1. 1. is an AP whose first term and common difference are 3 and 3 respectively.
2.
3. 2. is an AP whose first term and common difference are 7 and –2 respectively.
4.
5. 3. is an AP whose first term and common difference are –7 and 0 respectively.
• The general form of an AP can be written as a, a + d, a + 2d, a + 3d …, where a is the first term and d is the common difference.
• A given list of numbers i.e., a1, a2, a3 … forms an AP if ak+1ak is the same for all values of k.

Example 2:

Which of the following lists of numbers forms an AP? If it forms an AP, then write its next three terms.

(a) –4, 0, 4, 8, …

(b) 2, 4, 8, 16, …

Solution:

(a) –4, 0, 4,…

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