Directions: Find the missing number in the given series. 7, 11, 20, 45, 94, ____

The differences between the consecutive terms are successive multiples of three squared, calculated as 11 - 7 = 4 (which is incorrect for the pattern but leads into the next differences), 20 - 11 = 9, 45 - 20 = 25, and 94 - 45 = 49. Recognizing the underlying pattern, we apply the method of multiplying by three and subtracting an increasing odd number: (7 x 1) + 4 = 11, (11 x 2) - 2 = 20, (20 x 3) - 15 = 45, (45 x 4) - 86 = 94. Alternatively, adding the sum of squares of consecutive integers yields the missing term: 94 + 121 = 215.

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