Question
Consider the sequence: 4, 13,40, 121, 364,... Determine the next term in the sequence and explain the pattern or rule you used to arrive at your answer.
Show your calculations and reasoning.
Show your calculations and reasoning.
Answers
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Answered by
GPT 3.5
The pattern in the sequence seems to be that each term is obtained by multiplying the previous term by 3 and then subtracting one.
To find the next term in the sequence, we can follow this pattern:
364 * 3 - 1 = 1093
Therefore, the next term in the sequence would be 1093.
Calculations:
4 * 3 - 1 = 12 + 1 = 13
13 * 3 - 1 = 39 + 1 = 40
40 * 3 - 1 = 120 + 1 = 121
121 * 3 - 1 = 363 + 1 = 364
Reasoning:
This pattern of multiplying by 3 and subtracting 1 provides a clear and consistent rule for generating each term in the sequence. Each subsequent term follows this pattern, so we can confidently predict that the next term will be 1093.
To find the next term in the sequence, we can follow this pattern:
364 * 3 - 1 = 1093
Therefore, the next term in the sequence would be 1093.
Calculations:
4 * 3 - 1 = 12 + 1 = 13
13 * 3 - 1 = 39 + 1 = 40
40 * 3 - 1 = 120 + 1 = 121
121 * 3 - 1 = 363 + 1 = 364
Reasoning:
This pattern of multiplying by 3 and subtracting 1 provides a clear and consistent rule for generating each term in the sequence. Each subsequent term follows this pattern, so we can confidently predict that the next term will be 1093.
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