Look for a pattern and predict the next two numbers in each sequence.$2,3,5,8,12,\mathrm{....}$

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

Inductive reasoning is conclusions based on several past observations.

While looking for a pattern in the sequence$2,3,5,8,12\mathrm{....}$ reason inductively that is., we can conclude based on past observations

As,

$\begin{array}{l}2+0=2\\ 2+1=3\\ 3+2=5\\ 5+3=8\\ 8+4=12\end{array}$

So, the pattern of the sequence is that the natural numbers 1,2,3,4 and so on in order are added to each of the number to get the next number.

Since, the pattern of the sequence is that the natural numbers 1,2,3,4 and so on in order are added to each of the number to get the next number.

So, the next two term of the sequence will be, $12+5=17$and $17+6=23$

Therefore, the sequence will be $2,3,5,8,12,\underset{¯}{17},\underset{¯}{23},\mathrm{....}$.

Therefore, sequence with next two numbers is $2,3,5,8,12,\underset{¯}{17},\underset{¯}{23},\mathrm{....}$.