Understanding Number Series Patterns: Solving the Missing Number

This question asks us to find the next number in the given series: 8, 17, 36, 75, 154, ?. To solve this, we need to identify the underlying pattern or rule that connects consecutive terms in the number series.

Analyzing the Given Number Series

Let's look at the differences between consecutive terms or try to find a relationship involving multiplication and addition/subtraction.

• From 8 to 17: The difference is $17 - 8 = 9$. Alternatively, $8 \times 2 = 16$, and $16 + 1 = 17$.
• From 17 to 36: The difference is $36 - 17 = 19$. Alternatively, $17 \times 2 = 34$, and $34 + 2 = 36$.
• From 36 to 75: The difference is $75 - 36 = 39$. Alternatively, $36 \times 2 = 72$, and $72 + 3 = 75$.
• From 75 to 154: The difference is $154 - 75 = 79$. Alternatively, $75 \times 2 = 150$, and $150 + 4 = 154$.

We can observe a consistent pattern here. Each term is obtained by multiplying the previous term by 2 and then adding a number. The number being added increases sequentially: 1, 2, 3, 4. This is a common type of number series pattern.

Applying the Pattern to Find the Next Number

Following the identified pattern, the next step is to take the last known term, 154, multiply it by 2, and add the next number in the sequence (which is 5, after 4).

The calculation for the next term is:

Next term $= \text{Last term} \times 2 + \text{Next number to add}$

Next term $= 154 \times 2 + 5$

First, calculate the multiplication:

$154 \times 2 = 308$

Then, add the next number in the sequence:

$308 + 5 = 313$

So, the number that replaces the question mark (?) in the number series is 313.

Let's summarize the pattern application for each step:

Conclusion

Based on the consistent pattern of multiplying the previous term by 2 and adding an incrementally increasing number (1, 2, 3, 4, 5...), the next number in the series 8, 17, 36, 75, 154, ? is 313.

Revision Table: Number Series Pattern

Here's a quick look at the series and the rule applied:

Additional Information on Number Series Reasoning

Number series questions are common in reasoning and quantitative aptitude tests. They assess your ability to identify logical rules and patterns.

Common types of number series patterns include:

• Arithmetic Series: A constant difference between consecutive terms (e.g., 2, 5, 8, 11... difference is +3).
• Geometric Series: A constant ratio between consecutive terms (e.g., 3, 6, 12, 24... ratio is $\times 2$).
• Difference Series: The differences between consecutive terms form their own pattern (e.g., 1, 2, 4, 7, 11... differences are +1, +2, +3, +4...).
• Combination Series: Involves multiple operations, like the series we solved (multiplication and addition).
• Fibonacci Series: Each term is the sum of the two preceding terms (e.g., 0, 1, 1, 2, 3, 5, 8...).
• Prime Number Series: Series consists of prime numbers in order (e.g., 2, 3, 5, 7, 11...).
• Square/Cube Series: Terms are squares or cubes of natural numbers or follow a pattern involving squares/cubes.

To solve number series questions, practice identifying patterns by looking at differences, ratios, and combinations of operations between consecutive terms.