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.
is an AP whose first term and common difference are 3 and 3 respectively.
- 2.
is an AP whose first term and common difference are 7 and –2 respectively.
- 3.
is an AP whose first term and common difference are –7 and 0 respectively.
- 1.
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- 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+1 – ak 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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