Identify and extend the pattern to find the next number in this sequence: 56, 45, 34, 23, ...
A. 12
B. 13
C. 11
D. 10
Answer (2)
Calculate the difference between consecutive terms: 56 − 45 = 11 , 45 − 34 = 11 , 34 − 23 = 11 .
Identify the common difference as -11.
Subtract the common difference from the last term: 23 − 11 = 12 .
The next number in the sequence is 12 .
Explanation
Analyzing the Sequence We are given the sequence 56, 45, 34, 23, ... and we need to find the next number in the sequence.
Finding the Pattern To identify the pattern, let's find the difference between consecutive terms:
56 - 45 = 11
45 - 34 = 11
34 - 23 = 11
Since the difference is constant, this is an arithmetic sequence.
Calculating the Next Term The common difference between consecutive terms is -11. To find the next term, we subtract 11 from the last term in the sequence, which is 23. So, the next term is: 23 − 11 = 12
Final Answer Therefore, the next number in the sequence is 12.
Examples
Arithmetic sequences are useful in many real-life situations, such as predicting future values based on a consistent rate of change. For example, if you save a fixed amount of money each month, the total savings over time form an arithmetic sequence. Similarly, if a machine depreciates in value by a fixed amount each year, its value over time forms an arithmetic sequence. Understanding arithmetic sequences helps in financial planning, forecasting, and understanding linear growth or decay patterns.
The next number in the sequence 56, 45, 34, 23 is found by subtracting 11 from the last term, which gives us 12. Thus, the next number is 12. This sequence is an example of an arithmetic sequence, where each number decreases by 11.
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