Multiple choice general knowledge math & puzzles

1 , 2 , 4 , 13 , 31 , 112 , ?

  1. 213

  2. 224

  3. 729

  4. none
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sequence follows a pattern where each term is obtained by multiplying the previous term by an increasing integer and adding successive square numbers: 1×2+0²=2, 2×2+1²=5 (not 4), wait. The actual pattern appears to be: multiply by 2 and add squares in sequence 0, 1, 4, 9, 16... So: 1×2+0=2, 2×2+0=4, 4×3+1=13, 13×2+5=31, 31×3+19=112... The pattern gives 112×2+0=224.

AI explanation

To find the pattern in the given sequence, let's look at the differences between consecutive terms:

1, 2, 4, 13, 31, 112

The differences are:

1, 2, 9, 18, 81

Looking closely at the differences, we can see that they are increasing by a factor of 2 each time. Specifically, the differences are:

2 - 1 = 1 9 - 2 = 7 18 - 9 = 9 81 - 18 = 63

Now, let's add these differences to the previous term to get the next term in the sequence:

1 + 1 = 2 2 + 7 = 9 9 + 9 = 18 18 + 63 = 81

Adding these terms to the previous terms, we get the following sequence:

1, 2, 4, 13, 31, 112, 224

Therefore, the correct answer is B) 224.

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