In the sequence $6, 9, 14, x, 30, 41$, a possible value of $x$ is

Consider the differences between consecutive terms of the sequence $6, 9, 14, x, 30, 41$:

• $9 - 6 = 3$

• $14 - 9 = 5$

• $x - 14 = d_3$

• $30 - x = d_4$

• $41 - 30 = 11$

The differences form a sequence of consecutive odd numbers: $3, 5, 7, 9, 11$.

Setting $d_3 = 7$:

Verifying with the next term:

Alternatively, the general term can be written as $T_n = n^2 + 5$ for $n = 1, 2, 3, 4, 5, 6$:

• $T_1 = 1^2 + 5 = 6$

• $T_2 = 2^2 + 5 = 9$

• $T_3 = 3^2 + 5 = 14$

• $T_4 = 4^2 + 5 = 21$

• $T_5 = 5^2 + 5 = 30$

• $T_6 = 6^2 + 5 = 41$

Hence, the correct value of $x$ is 21, which corresponds to option (B).