Multiple choice

Find the missing term in the series. 3/4, 7/13, 15/40, 31/121, ?, 127/1093

  1. 61/120

  2. 94/81

  3. 63/364

  4. 45/325
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C Correct answer
Explanation

The numerators follow the pattern 2^n - 1 (3, 7, 15, 31, 63, 127). The denominators follow the recurrence relation d(n) = 3*d(n-1) + 1 (4, 13, 40, 121, 364, 1093). Thus, the missing term is 63/364.

AI explanation

The numerators form a pattern where each number is multiplied by 2, and then 1 is added to the product. The denominators follow a pattern of multiplying by 3 and then subtracting 2. For the numerator, 31 multiplied by 2 is 62, plus 1 is 63. For the denominator, 121 multiplied by 3 is 363, minus 2 is 361, but since the final term denominator is 1093, we see the actual pattern is multiplying by 3 and adding 1; 121 multiplied by 3 is 363, plus 1 is 364. The result is 63/364.

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