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If you are given the following table, which the most efficient counting method would you use to find the 105th term in the pattern? Input (n) Output f(n) 1 1 2 4 16 64 Geometric recursive formula Arithmetic explicit formula Geometric explicit formula Arithmetic recursive formula 3 4 a Ob C Od

If you are given the following table, which the most efficient counting method would you use to find the 105th term in the pattern? Input (n) Output f(n) 1 1 2 4 16 64 Geometric recursive formula Arithmetic explicit formula Geometric explicit formula Arithmetic recursive formula 3 4 a Ob C Od

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Finding the Most Efficient Counting Method for a Pattern** The table below provides input values (n) and their corresponding output values (f(n)). | Input (n) | Output (f(n)) | |-----------|------------| | 1 | 1 | | 2 | 4 | | 3 | 16 | | 4 | 64 | Based on the table, determine which counting method is most efficient to find the 105th term in the pattern: - a. Geometric recursive formula - b. Arithmetic explicit formula - c. Geometric explicit formula - d. Arithmetic recursive formula After analyzing the pattern of the output values in the table, select the appropriate answer by evaluating the efficiency and correctness of each method listed. **Analysis of the Table:** - The outputs do not follow a consistent arithmetic increase (i.e., they are not adding the same value each time), suggesting an arithmetic formula is not suitable. - The outputs grow significantly faster, indicating an exponential or geometric increase. Identify the correct formula to efficiently calculate the 105th term based on the observed pattern of the outputs.
Transcribed Image Text:**Finding the Most Efficient Counting Method for a Pattern** The table below provides input values (n) and their corresponding output values (f(n)). | Input (n) | Output (f(n)) | |-----------|------------| | 1 | 1 | | 2 | 4 | | 3 | 16 | | 4 | 64 | Based on the table, determine which counting method is most efficient to find the 105th term in the pattern: - a. Geometric recursive formula - b. Arithmetic explicit formula - c. Geometric explicit formula - d. Arithmetic recursive formula After analyzing the pattern of the output values in the table, select the appropriate answer by evaluating the efficiency and correctness of each method listed. **Analysis of the Table:** - The outputs do not follow a consistent arithmetic increase (i.e., they are not adding the same value each time), suggesting an arithmetic formula is not suitable. - The outputs grow significantly faster, indicating an exponential or geometric increase. Identify the correct formula to efficiently calculate the 105th term based on the observed pattern of the outputs.
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