Multiple choice

Directions: Find the next term of the series. 13, 25, 51, 101, 203, ________

  1. 405

  2. 406

  3. 407

  4. 411
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A Correct answer
Explanation

The pattern is: 13 * 2 - 1 = 25, 25 * 2 + 1 = 51, 51 * 2 - 1 = 101, 101 * 2 + 1 = 203. The next term is 203 * 2 - 1 = 405.

AI explanation

We can observe two alternating patterns where the operations alternate between multiplying by 2 and adding 2. From 13, multiplying by 2 gives 26, and subtracting 1 gives 25; from 25, multiplying by 2 gives 50, and adding 1 gives 51. This pattern of multiplying by 2 and then alternately subtracting 1 and adding 1 continues, so 203 multiplied by 2 yields 406, and then adding 1 is not the next operation. Another way to see it is through differences: 25 - 13 = 12, 51 - 25 = 26, 101 - 51 = 50, 203 - 101 = 102; applying the pattern, the next difference is calculated to result in 405.

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