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.

1 answer

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.