Analyzing the Number Series Pattern

The question asks us to find the number that logically follows in the given numerical sequence: $1, 3, 9, 27, ?$

To solve this, we need to identify the pattern or rule governing the series.

Identifying the Series Progression

Let's examine the relationship between consecutive terms in the series:

• The first term is 1.
• The second term is 3. The relationship between the first and second term is $1 \times 3 = 3$.
• The third term is 9. The relationship between the second and third term is $3 \times 3 = 9$.
• The fourth term is 27. The relationship between the third and fourth term is $9 \times 3 = 27$.

It is clear that each term in the series is obtained by multiplying the previous term by 3.

Calculating the Missing Number

Following the established pattern, the next number in the series should be the fourth term multiplied by 3.

The fourth term is 27.

Therefore, the missing number is calculated as:

$$ 27 \times 3 $$

Performing the multiplication:

$$ 27 \times 3 = 81 $$

Alternatively, we can see the series as powers of 3:

• $1 = 3^0$
• $3 = 3^1$
• $9 = 3^2$
• $27 = 3^3$

The next term would be $3^4$.

$$ 3^4 = 3 \times 3 \times 3 \times 3 = 81 $$

Conclusion

The number that replaces the question mark (?) in the series $1, 3, 9, 27, ?$ is 81.