Multiple choice

Directions: Find the missing term in the following series. 1, 5, 14, 30, 55, 91, ____

  1. 130

  2. 140

  3. 150

  4. 160
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B Correct answer
Explanation

The differences between consecutive terms are: 4, 9, 16, 25, 36. These are squares of 2, 3, 4, 5, 6. The next difference should be 7^2 = 49. Therefore, 91 + 49 = 140.

AI explanation

The differences between the successive terms of the series are calculated using the method of successive differences. The first differences are 4, 9, 16, 25, 36, which are the perfect squares of 2, 3, 4, 5 and 6 respectively. Following this pattern, the next difference to be added to 91 is 49, the square of 7. Adding 49 to 91 gives the missing term, so the result is 140.

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