If you're seeing this message, it means we're having trouble loading external resources on our website.
If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Contemporary Abstract Algebra
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Publisher:Cengage Learning
Algebra And Trigonometry (11th Edition)
Introduction to Linear Algebra, Fifth Edition
Publisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
Algebra and Trigonometry (6th Edition)
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Contemporary Abstract Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra And Trigonometry (11th Edition)
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Introduction to Linear Algebra, Fifth Edition
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
Inductive Reasoning is a reasoning that is based on patterns you observe. If you observe a pattern in a sequence, you can use inductive reasoning to decide the next successive terms of the sequence.
A conclusion you reach using inductive reasoning is called a conjecture . Examining several specific situations to arrive at a conjecture is called inductive reasoning.
Inductive reasoning is different than proof. It can be used to make predictions, but it should never be used to make certain claims. For that, you need deductive reasoning and mathematical proof.
Example :
Find a pattern for the sequence. Use the pattern to find the next three terms in the sequence.
2 , 4 , 7 , 11 , ...
From the given sequence we have,
4 − 2 = 2 7 − 4 = 3 11 − 7 = 4
Observe that, the difference between 4 and 2 is 2 and the difference between 7 and 4 is 3 and so on.
The difference between the consecutive numbers is increased by 1 .
So, add 5 to 11 , to get the next term of the sequence.
11 + 5 = 16
Now add 6 to get the next term and so on.
16 + 6 = 22 22 + 7 = 29
Therefore, the next three terms in the sequence will be 16 , 22 , and 29 .