Look for a pattern and predict the next two numbers in each sequence.

2,20,10,100,50,....

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 sequences 2, 20, 10, 100, 50, ... reason inductively that is., we can conclude based on past observations.

Let terms be

$\begin{array}{l}{T}_0=2\\ T_1=20\\ T_2=10\\ T_3=100\\ T_4=50\end{array}$

Consider the alternate terms$T_0=2,T_2=10,T_4=50$

Here each next term is multiplied by 5.

So, the next term $T_6=50\times 5=250$

Now,

Consider the alternate terms $T_1=20,T_3=100$.

Here also each next term is multiplied by 5.

Since the pattern of the sequence is that two individual sequences {$T_0=2,T_2=10,T_4=50$} and {$T_1=20,T_3=100$} have terms such that the next term is multiplied by 5.

So, the next two term of the sequence will be,

$T_6=50\times 5=250$and$T_5=100\times 5=500$

Therefore, the sequence will be $2,20,10,100,50,\underset{¯}{500},\underset{¯}{250}\mathrm{...}$.