91Ó°ÊÓ

Deductive reasoning is conclusions based on accepted statements like a theorem, postulate, facts etc.

Inductive reasoning is conclusions based on several past observations.

Here the given sequence can be written as,

$1,\text{ }4,\text{ }9,\text{ }16,\text{ }\mathrm{....}≈1^2,\text{ }{2}^2,\text{ }{3}^2,\text{ }{4}^2,\text{ }\mathrm{....}$

Therefore, while looking for a pattern we can reason inductively that is., we can conclude based on past observations. So, the following numbers are the sequence of numbers.

Since the sequence is squares of natural numbers, so, the next two terms of the sequence according to the pattern is $5^2{\text{ a²Ô»å6}}^2$which is equal to 25 and 36.

So, the sequence will be, $1,\text{ }4,\text{ }16,\text{ }64,\text{ }\underset{¯}{25},\text{ }\underset{¯}{36},\text{ }\mathrm{...}$.

Therefore, the sequence with the next two numbers is $1,\text{ }4,\text{ }16,\text{ }64,\text{ }\underset{¯}{25},\text{ }\underset{¯}{36},\text{ }\mathrm{...}$..