GATE CS 2024 Set 2 Q.5: Analytical and Logical Reasoning

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

Official answer and solution

Solution

Examine the consecutive differences between terms (or notice $a_n = n^2 + 5$ ).

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

$9 - 6 = 3$
$14 - 9 = 5$
Following the consecutive odd differences $+3, +5, +7, +9, +11$ $+ 3, + 5, + 7, + 9, + 11$ :
- $x = 14 + 7 = 21$
- $21 + 9 = 30$
- $30 + 11 = 41$

(Equivalently, the $n$ -th term is $n^2 + 5$ for $n = 1, 2, 3, 4, 5, 6$ , giving $x = 4^2 + 5 = 21$ .)

Final answer

Option (B)

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