Analyzing the Number Series Pattern

We are given the number series: 79, 81, 84, 89, 96, ?

To find the missing number that replaces the question mark, we need to carefully analyze the relationship or pattern between consecutive terms in this number series.

Finding the Differences Between Terms

A common approach for number series questions is to calculate the difference between adjacent terms. Let's do that for the given series:

• Difference between the 2nd term (81) and the 1st term (79): ${81 - 79 = 2}$
• Difference between the 3rd term (84) and the 2nd term (81): ${84 - 81 = 3}$
• Difference between the 4th term (89) and the 3rd term (84): ${89 - 84 = 5}$
• Difference between the 5th term (96) and the 4th term (89): ${96 - 89 = 7}$

The sequence of differences we obtained is 2, 3, 5, 7.

Identifying the Pattern in Differences

Now, let's look for a pattern in this new sequence of differences: 2, 3, 5, 7.

These numbers are not consecutive integers, nor are they increasing by a constant value.

However, if we examine these numbers closely, we can see that they are the first four prime numbers in ascending order.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The sequence of prime numbers begins with 2, 3, 5, 7, 11, 13, 17, and so on.

Since the differences in the original series follow the pattern of consecutive prime numbers (2, 3, 5, 7), the next difference should be the next prime number after 7, which is 11.

Calculating the Next Term

To find the next term in the original series (the one that replaces the question mark), we must add the next expected difference (11) to the last term given in the series (96).

Next Term $= \text{Last Term} + \text{Next Difference}$

Next Term $= 96 + 11$

Next Term $= 107$

Thus, the number that should replace the question mark in the series 79, 81, 84, 89, 96, ? is 107.

Revision Table: Number Series Pattern Summary

Additional Information: Exploring Number Series Types

Number series problems often appear in aptitude and reasoning tests. They can follow various patterns, including:

• Arithmetic Progression: The difference between consecutive terms is constant.
• Geometric Progression: Each term is found by multiplying the previous one by a fixed, non-zero number.
• Difference Series: The differences between consecutive terms form a pattern (as seen in this problem). The pattern of differences itself can be arithmetic, geometric, or follow another rule (like prime numbers, squares, cubes, etc.).
• Ratio Series: The ratio between consecutive terms forms a pattern.
• Mixed Series: A combination of two or more different patterns within a single series.
• Fibonacci or Similar Series: Each term is the sum of the two preceding terms (or follows a similar recursive rule).

Identifying the pattern, whether it's in the terms themselves, their differences, ratios, or a combination, is key to solving number series questions.