Find the Missing Number in Series: 16, 32, 64, 128, ?, 512

The question asks us to identify the missing number in the given number series: 16, 32, 64, 128, ?, 512.

To find the missing number in a series, we need to look for a pattern or rule that connects the numbers together. Let's examine the relationship between consecutive terms in this specific series.

Analyzing the Number Series Pattern

Let's observe how the numbers change from one term to the next:

• From 16 to 32: $32 = 16 \times 2$
• From 32 to 64: $64 = 32 \times 2$
• From 64 to 128: $128 = 64 \times 2$

It appears that each term in the series is obtained by multiplying the previous term by 2. This type of series is known as a geometric series.

Calculating the Missing Number

Following the pattern identified, the missing number will be the term after 128, which is found by multiplying 128 by 2.

Missing Number = $128 \times 2$

Calculation:

$128 \times 2 = 256$

So, the missing number is 256.

Verifying the Pattern

Let's verify if the next term in the series, 512, follows the same pattern with our calculated missing number, 256.

If the missing number is 256, then the next term should be $256 \times 2$.

$256 \times 2 = 512$

This matches the last number given in the series (512). This confirms that our identified pattern and the calculated missing number are correct.

Conclusion on the Missing Number

The pattern in the series 16, 32, 64, 128, ?, 512 is that each term is double the previous term. By applying this rule, we found that the missing number is 256.

The complete series is therefore 16, 32, 64, 128, 256, 512.

Revision Table: Number Series Pattern

Additional Information on Number Series

Number series questions test your ability to find patterns in sequences of numbers. Common patterns include:

• Arithmetic Progression: A constant difference between consecutive terms (e.g., 2, 4, 6, 8...).
• Geometric Progression: A constant ratio between consecutive terms (e.g., 3, 9, 27, 81...).
• Difference Series: The difference between consecutive terms forms another pattern (e.g., 1, 2, 4, 7, 11... where differences are +1, +2, +3, +4...).
• Mixed Series: Combination of different patterns.
• Fibonacci Series: Each term is the sum of the two preceding terms (e.g., 0, 1, 1, 2, 3, 5, 8...).

Solving number series problems requires careful observation and testing different potential rules.