Multiple choice

The seventh term in the series 5, 13, 29, 61, ... is ________________.

  1. 97

  2. 191

  3. 253

  4. 509
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D Correct answer
Explanation

The pattern is a_n = 2*a_{n-1} + 3. 5, 13, 29, 61, 125, 253, 509. The seventh term is 509.

AI explanation

The difference between the terms doubles successively, starting with 8. We see that 5 plus 8 is 13, 13 plus 16 is 29, and 29 plus 32 is 61. To find the fifth term, add 64 to 61 to get 125, and then add 128 to 125 to find the sixth term of 253. Finally, add 256 to 253 to get the seventh term of 509.

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