GATE CS 2024 Set 2 Q5 — General Aptitude

Let us analyze the differences between consecutive terms of the given sequence: $6, 9, 14, x, 30, 41$.

Let the differences between consecutive terms be denoted as $d_1, d_2, d_3, d_4, d_5$:

• $d_1 = 9 - 6 = 3$
• $d_2 = 14 - 9 = 5$
• $d_3 = x - 14$
• $d_4 = 30 - x$
• $d_5 = 41 - 30 = 11$

The known differences are $3, 5, \dots, \dots, 11$. This sequence of differences represents consecutive odd numbers starting from $3$:

$3, 5, 7, 9, 11$

Applying this pattern, we find $x$ by adding the next odd number ($7$) to the third term:

We can verify this value with the subsequent term:

Since $9$ is indeed the next consecutive odd number, the pattern is consistent. Thus, the value of $x$ is $21$.