Finding the Missing Number in a Series

The question asks us to find the missing number in the given series: 11, 12, 14, 17, 21, ?

To solve this number series problem, we need to identify the pattern or rule that governs the sequence of numbers. Let's examine the differences between consecutive terms in the series.

Analyzing the Pattern in the Number Series

We will calculate the difference between each term and the preceding term:

• Difference between the 2nd and 1st term: $12 - 11 = 1$
• Difference between the 3rd and 2nd term: $14 - 12 = 2$
• Difference between the 4th and 3rd term: $17 - 14 = 3$
• Difference between the 5th and 4th term: $21 - 17 = 4$

Let's list these differences:

We observe that the differences between consecutive terms are increasing by 1 each time (1, 2, 3, 4). This sequence of differences (1, 2, 3, 4, ...) is an arithmetic progression with a common difference of 1.

Predicting the Next Difference

Following this pattern, the next difference in the series should be the next term in the sequence of differences (1, 2, 3, 4, ...). The next number after 4 in this sequence is 5.

So, the difference between the missing number (the 6th term) and the last given number (the 5th term, which is 21) should be $+5$.

Calculating the Missing Number

To find the missing number, we add the next expected difference (+5) to the last number in the series (21).

Missing Number = Last Term + Next Difference

Missing Number = $21 + 5$

Missing Number = $26$

Thus, the missing number in the series 11, 12, 14, 17, 21, ? is 26.

Conclusion for the Number Series

The pattern in the series is that each term is obtained by adding an increasing number to the previous term, starting with +1 and increasing the increment by 1 each time. The missing number is 26.

Revision Table: Number Series Patterns

Additional Information on Solving Number Series

Solving number series questions often involves looking for common patterns. Here are some strategies:

• Calculate differences between consecutive terms. Check if these differences form an arithmetic series or another simple pattern.
• Calculate ratios between consecutive terms. Check if these ratios form a geometric series.
• Look for alternating patterns (e.g., two separate series interwoven).
• Consider squares, cubes, or other powers of numbers.
• Think about prime numbers or other specific number sequences.
• Sometimes, the pattern involves operations (addition, subtraction, multiplication, division) or a combination of operations.

Practicing different types of number series helps in quickly recognizing patterns during exams.