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. 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 a_k+1 – a_k 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,…