The correct alternative that will continue the same pattern is 17. Hence the correct option is c.
The given series follows a pattern where each term is constructed by adding 2 to the numerator and 4 to the denominator of the previous term. Starting with the initial term, 2/3, the next term is obtained by adding 2 to the numerator (2 + 2 = 4) and 4 to the denominator (3 + 4 = 7), resulting in 4/7. This pattern continues for subsequent terms.
To find the missing term after 4/7, we apply the same logic: add 2 to the numerator (4 + 2 = 6) and 4 to the denominator (7 + 4 = 11). Therefore, the missing term in the series is 6/11.
The complete series is then 2/3, 4/7, 6/11, 11/21, 16/31. Among the provided options, 17 (option c) stands out as the correct term following the established pattern, thus completing the sequence and maintaining the consistent progression observed in the given number series. Hence the correct option is c.