Question 6

Explanation

To find the pattern of this sequence, we need to look at the difference between consecutive terms. Let's dissect the changes one by one.

Our initial sequence is:

Now, observe the jump in addition from one number to the next:

• From $2$ to $3$, it increases by $1$.
• From $3$ to $5$, it increases by $2$.
• From $5$ to $9$, it increases by $4$.
• From $9$ to $17$, it increases by $8$.

If we write down the addition pattern, we get a new series:

It is clear that each addition is double the previous addition (or powers of 2: $2^0, 2^1, 2^2, 2^3$).

Therefore, the next addition must be double of $8$, which is $16$.

Let's calculate the next term:

So, the correct number to fill the sequence is 33.