2,3,5,7,11... What is the inductive reasoning?
these numbers are all primes. Using that pattern, the sequence continues with
13,17,23,29,...
Or, you could say that the numbers differ by
1,2,2,4,...
So, the pattern of differences could be
1 1, 2 2's, 4 4's, 6 6's, ... and the sequence would continue
15,19,23,29,35,41,47,...
You can always come up with a variety of patterns for just a few data points. In this case, the familiar sequence of primes seems to be the simplest.
The sequence you presented, 2, 3, 5, 7, 11, is a series of prime numbers. Inductive reasoning is a type of reasoning that involves making generalizations based on observations or patterns.
To determine the inductive reasoning behind this sequence, we can observe that each number in the series is a prime number. In mathematics, a prime number is a natural number greater than 1 that cannot be divided evenly by any other numbers except 1 and itself.
Therefore, the inductive reasoning behind this sequence is that each subsequent term is the next prime number in the series, following the rule of prime numbers.