Understanding Number Series Patterns

Let's analyze the given number series to find the underlying pattern and determine the next term. The series is:

11, 15, 12, 16, 13, ?

We need to look at the relationship between consecutive numbers in the series.

• From the 1st term (11) to the 2nd term (15): $15 - 11 = 4$. The operation is $+4$.
• From the 2nd term (15) to the 3rd term (12): $12 - 15 = -3$. The operation is $-3$.
• From the 3rd term (12) to the 4th term (16): $16 - 12 = 4$. The operation is $+4$.
• From the 4th term (16) to the 5th term (13): $13 - 16 = -3$. The operation is $-3$.

It appears there is a repeating pattern of operations: $+4$, then $-3$, then $+4$, then $-3$, and so on. The next operation in the sequence should be $+4$.

To find the next term in the series, we apply the next operation ($+4$) to the last given term (13).

Next term $= 13 + 4 = 17$.

So, the number that replaces the question mark is 17.

Let's summarize the pattern in a table:

The series with the next term is 11, 15, 12, 16, 13, 17.

Revision Table: Analyzing Number Series

Additional Information: Types of Number Series Patterns

Number series problems can involve various types of patterns. Some common ones include:

• Arithmetic Series: Each term is obtained by adding or subtracting a constant value to the previous term (e.g., 2, 4, 6, 8, ... pattern is $+2$).
• Geometric Series: Each term is obtained by multiplying or dividing the previous term by a constant value (e.g., 3, 6, 12, 24, ... pattern is $\times 2$).
• Mixed Series: The pattern involves a combination of operations, often alternating (like the $+4, -3$ pattern in this problem).
• Difference Series: The pattern is found by looking at the differences between consecutive terms. Sometimes, the pattern is in the differences of the differences (second-order differences).
• Square or Cube Series: Terms are related to squares or cubes of numbers, often with an addition or subtraction (e.g., $1^2+1, 2^2+1, 3^2+1$, which is 2, 5, 10, ...).
• Fibonacci-like Series: Each term is the sum of the two preceding terms (e.g., 1, 1, 2, 3, 5, 8, ...).

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