Arthimatic progression

CLASS-X MATHEMATICS

ARITHMETIC PROGRESSION

Learning Objectives

Students will be able to

• recall some patterns which occur in their day to day life.
• know the condition when the pattern will be in arithmetic progression.
• know various terms associated with AP, i.e 1st term and common difference.
• understand different types of AP, finite & infinite.
• understand the formula to find nth term and sum of n terms of an AP.
• apply the knowledge of finding nth term and sum of n terms of an AP in solving day to day life problems.

Sequence

• A sequence is a set of numbers written in a particular order
• Examples of sequence:
• 1, 3, 5, 7, 9, . . . .
• 1, 4, 9, 16, 25, . . . .
• 1, −1, 1, −1, 1, −1, . . . ,
• 1, 3, 5, 9

Series

• A series is something we obtain from a sequence by adding all the terms together.
• For example, let us consider the sequence of numbers 1, 2, 3, 4, 5, 6, . . ., n .
• Then S1 = 1, as it is the sum of just the first term on its own.
• The sum of the first two terms is S2 = 1 + 2 = 3.
• Continuing, we get S3 = 1 + 2 + 3 = 6 , S4 = 1 + 2 + 3 + 4 = 10 ,