Multiple choice

Directions: Find the missing number in the following series. 4, 16, 57, 187, 586, ?

  1. 1645

  2. 1736

  3. 1794

  4. 1823

  5. 1856
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C Correct answer
Explanation

The pattern is: 4*3+4=16, 16*3+9=57, 57*3+16=187, 187*3+25=586. The sequence adds squares of consecutive integers (2^2, 3^2, 4^2, 5^2). The next step is 586*3 + 6^2 = 1758 + 36 = 1794.

AI explanation

The differences between the terms follow a pattern where each difference is multiplied by 3 and then an increasing integer is subtracted. The differences are 12, 41, 130, and 399, where 12 times 3 plus 5 equals 41, 41 times 3 plus 7 equals 130, and 130 times 3 plus 9 equals 399. The next difference is 399 times 3 plus 11, which equals 1208, so adding this to 586 gives 1794. The missing number is 1794.

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