The human brain has been wired to recognize patterns since ancient times. Whether it is tracking the movement of wild animals or predicting the change of seasons, pattern recognition has been crucial for human survival. Similarly, modern-day problem-solving involves identifying patterns and applying logical deduction to find solutions. One such problem that requires pattern recognition is the “Missing Number Problem.” In this article, we will explore how to crack the code and find the missing number in the sequence 7, 10, 16, 28.
Before we dive into the solution, let’s start by understanding what constitutes a sequence. In mathematics, a sequence is a set of numbers arranged in a particular order. Each number in a series is called a term, and the position of each term is denoted by the term number. For example, in the sequence 2, 4, 6, 8, 10, the first term is 2, the second term is 4, and so on.
Now coming back to our problem, the given sequence is 7, 10, 16, 28. We are supposed to find the next number in the sequence i.e., the missing number. This is easier said than done, as there can be numerous sequences that can fit the pattern. However, our task is made easier because the given sequence has a clear pattern. If we observe carefully, we can see that the difference between successive terms in the sequence is not constant. In other words, there is no common difference between the terms.
So, how do we proceed? We need to look for a pattern that can give us an insight into the next term in the sequence. One approach is to identify the relationship between each term and the position of the term in the sequence. For instance, in the sequence 1, 4, 9, 16, 25, the terms are the squares of the natural numbers 1, 2, 3, 4, and 5 respectively. Similarly, in the sequence 2, 6, 18, 54, each term is found by multiplying the previous term by 3.
However, in our current problem, there is no clear relationship between the terms and their position in the sequence. In such a scenario, we need to look for other patterns that may help us find the missing number. One such approach is to look for patterns in the difference between successive terms. If we plot the differences, we may be able to identify a pattern that can help us find the next term.
Let’s take a look at the sequence again and calculate the differences between successive terms:
– The difference between the second term (10) and the first term (7) is 3.
– The difference between the third term (16) and the second term (10) is 6.
– The difference between the fourth term (28) and the third term (16) is 12.
We can observe that the differences themselves form a pattern. Specifically, the differences are increasing by multiples of 3 i.e., 3, 6, 12. This gives us a clue into the missing number. To find the next term, we need to add the next multiple of 3 to the last difference, which is 12. The next multiple of 3 after 12 is 15. Therefore, the missing number in the sequence 7, 10, 16, 28 is 43.
In summary, cracking the code and finding the missing number in a sequence requires careful observation and pattern recognition. In some cases, the relationship between the terms and their position in the sequence may provide a clue. In other cases, looking at the differences between successive terms may reveal a pattern. By using logical deduction and reasoning, we can arrive at the correct answer and solve the problem.