Multiple choice

Given the following series, determine which one does not follow the pattern "Each term is double the previous term plus one." A: 3, 7, 15, 31, 63, 127 B: 5, 13, 29, 61, 125 C: 1, 3, 7, 15, 31, 63 Which of the following series does not follow the given pattern?

  1. Only A

  2. Only B

  3. Both A and B

  4. Both B and C

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pattern: x(n+1) = 2*x(n) + 1. Series A: 3*2+1=7, 7*2+1=15, 15*2+1=31, 31*2+1=63, 63*2+1=127 (Follows). Series B: 5*2+1=11 (not 13). Series C: 1*2+1=3, 3*2+1=7, 7*2+1=15, 15*2+1=31, 31*2+1=63 (Follows). Only B fails.

AI explanation

To verify the given rule, each term must be multiplied by two and then increased by one to obtain the next term in the sequence. In series A, multiplying 3 by 2 and adding 1 yields 7, and this logic correctly continues for all following terms up to 127. In series C, applying the rule to 1 correctly produces the rest of the sequence. In series B, multiplying 5 by 2 and adding 1 gives 11, which proves that 13 is the incorrect term, meaning only series B does not follow the pattern.

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