Solving the Series: 8 24 12 36 18 54 – Unveiling the Missing Number

Sequences can often appear mysterious, but by analyzing the underlying patterns, we can uncover the solution with ease. In this article, we will delve into the pattern of the series 8 24 12 36 18 54. We will break down the process step by step, explaining the logic and mathematics behind the sequence. By the end of this article, you will be able to identify the missing number and understand how to solve similar sequence problems.

Understanding the Series

Let's start with the given series: 8 24 12 36 18 54. To find the missing number, we need to identify the pattern that governs the sequence.

Pattern Analysis

The pattern alternates between multiplication by 3 and division by 2:

To get from the first number to the second number (8 to 24), we multiply by 3. To get from the second number to the third number (24 to 12), we divide by 2. To get from the third number to the fourth number (12 to 36), we multiply by 3. To get from the fourth number to the fifth number (36 to 18), we divide by 2. To get from the fifth number to the sixth number (18 to 54), we multiply by 3.

Following this pattern, the next step should be a division by 2.

Solving for the Missing Number

Starting from the last given number, 54:

54 ÷ 2 27

The missing number in the series is 27.

The Complete Series

The complete series following the identified pattern would be:

8 24 (8 × 3) 12 (24 ÷ 2) 36 (12 × 3) 18 (36 ÷ 2) 54 (18 × 3) 27 (54 ÷ 2)

Conclusion

In summary, the missing number in the series 8 24 12 36 18 54 is 27. The series follows a pattern of alternating multiplication by 3 and division by 2. By understanding this pattern, you can solve similar sequence problems and identify missing numbers in series.

Frequently Asked Questions

What is the missing number in the series 8 24 12 36 18 54?

The missing number in the series is 27. The pattern alternates between multiplication by 3 and division by 2.

How do you solve a sequence with alternating operations?

Identify the sequence of operations (e.g., multiply by 3, divide by 2). Apply these operations step by step to find the missing number.

Are there different techniques to solve sequence problems?

Yes, there are several techniques. Familiarity with patterns, sequence types, and algebraic manipulation can help in solving sequence problems systematically.

Related Patterns and Problems

Pattern Identification

Gather a variety of sequence problems and analyze them to recognize different patterns. Practice with various types of sequences (arithmetic, geometric, mixed operations) to improve your problem-solving skills.

Pattern-Based Exercises

Work on exercises that involve identifying and solving sequences based on different patterns. This will help reinforce your understanding and improve your ability to solve these types of problems.