In the following question, select the missing number from the given series.
9, 19, 37, 75, 149, ?

Question

In the following question, select the missing number from the given series.9, 19, 37, 75, 149, ?

Prepp Team · Accepted Answer

Understanding Number Series and Finding the Pattern

Number series questions are common in aptitude tests. They require you to identify a specific pattern or rule that connects the numbers in the given sequence. Once the pattern is found, you can determine the missing number.

The given series is:

9, 19, 37, 75, 149, ?

Analyzing the Given Number Series

Let's look at the relationship between consecutive terms in the series to find the pattern.

From 9 to 19: We can see that $9 \times 2 = 18$, and $18 + 1 = 19$.
From 19 to 37: Now consider $19 \times 2 = 38$. To get 37, we need to subtract 1: $38 - 1 = 37$.
From 37 to 75: Let's continue with the pattern. $37 \times 2 = 74$. To get 75, we add 1: $74 + 1 = 75$.
From 75 to 149: Following the pattern, $75 \times 2 = 150$. To get 149, we subtract 1: $150 - 1 = 149$.

Identifying the Pattern in the Series

Based on the analysis above, we can clearly see a repeating pattern:

Each term is obtained by multiplying the previous term by 2, and then alternately adding 1 and subtracting 1.

The operations are $+1, -1, +1, -1, \dots$

Step	Operation	Calculation	Resulting Term
1	Starting term		9
2	Previous term $\times 2 + 1$	$9 \times 2 + 1$	19
3	Previous term $\times 2 - 1$	$19 \times 2 - 1$	37
4	Previous term $\times 2 + 1$	$37 \times 2 + 1$	75
5	Previous term $\times 2 - 1$	$75 \times 2 - 1$	149

Calculating the Missing Number

The last operation performed was subtracting 1 to get 149. According to the pattern, the next operation should be adding 1.

So, to find the missing number, we apply the rule to the last known term (149) with the next operation (+1).

Missing Number = $149 \times 2 + 1$

Missing Number = $298 + 1$

Missing Number = $299$

Therefore, the missing number in the series is 299.

Revision Table: Key Concepts for Number Series

Concept	Description	Example Pattern Types
Identifying Pattern	Looking for mathematical relationships between consecutive terms (addition, subtraction, multiplication, division, squares, cubes, etc.).	Arithmetic progression, Geometric progression, Difference series, Alternating series, Mixed series.
Step-by-Step Analysis	Breaking down the series to find the rule applied from one term to the next.	Calculating differences, ratios, or applying operations sequentially.
Alternating Patterns	Patterns where the rule or operation changes back and forth between terms.	Example: $+2, -1, +2, -1$ or $\times 2 + 1, \times 2 - 1$.

Additional Information: Strategies for Solving Number Series

Solving number series problems often requires practice and recognizing common patterns. Here are a few strategies that can be helpful:

Look at Differences: Calculate the difference between consecutive terms. If the differences form a simple pattern (like an arithmetic series), you've found a key part of the rule.
Look at Ratios: If the numbers are increasing or decreasing rapidly, consider multiplication or division patterns. Calculate the ratio between consecutive terms.
Check for Squares and Cubes: Some series involve perfect squares, cubes, or numbers close to them (e.g., $n^2 \pm k$ or $n^3 \pm k$).
Consider Alternating Patterns: Sometimes, the pattern applies to alternate terms or involves alternating operations, as seen in this problem.
Combine Operations: Many complex series involve a combination of operations, like the multiply-and-add/subtract pattern shown here.
Practice: The more series you solve, the better you become at recognizing common patterns quickly.