Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number or item in the sequence. 1 2 4 7 11 16 22 29

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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 .