If the following series continues the same pattern, what is the next number in the series 1, 10, 7, 16?
Answer (2)
Calculate the differences between consecutive terms: 10-1 = 9, 7-10 = -3, 16-7 = 9.
Observe the pattern in the differences: 9, -3, 9, ...
Predict the next difference: -3.
Add the predicted difference to the last term: 16 + (-3) = 13. The next number in the series is 13 .
Explanation
Understanding the Problem We are given the series 1, 10, 7, 16 and asked to find the next number in the series, assuming the pattern continues.
Calculating Differences To identify the pattern, let's calculate the differences between consecutive terms:
10 - 1 = 9 7 - 10 = -3 16 - 7 = 9
Identifying the Pattern The differences between consecutive terms are 9, -3, 9. This suggests that the pattern of differences repeats every two terms. Therefore, the next difference should be -3.
Finding the Next Number To find the next number in the series, we add the next difference (-3) to the last term (16):
16 + (-3) = 13
Conclusion Therefore, the next number in the series is 13.
Examples
Understanding number patterns is useful in many real-life situations, such as predicting trends in data, understanding financial investments, or even in cryptography. For example, if you observe a pattern in stock prices, you might use it to make informed decisions about when to buy or sell. Similarly, understanding patterns can help in identifying anomalies or errors in data sets.
The next number in the series 1, 10, 7, 16 is 13. This conclusion is reached by observing the pattern in the differences between consecutive terms, which alternate between 9 and -3. Thus, the addition of -3 to the last term (16) results in the next term being 13.
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