GATE CS 2012 Q65 — General Aptitude

To find the next term in the sequence $\text{AD, CG, FK, JP}$, we analyze the patterns of the first and second letters of each term separately by converting them to their alphabetical positions ($A=1, B=2, \dots, Z=26$).

1. First Letter Pattern:

The first letters are $\text{A, C, F, J}$:

• $\text{A} \xrightarrow{+2} \text{C}$ (Positions: $1 \xrightarrow{+2} 3$)
• $\text{C} \xrightarrow{+3} \text{F}$ (Positions: $3 \xrightarrow{+3} 6$)
• $\text{F} \xrightarrow{+4} \text{J}$ (Positions: $6 \xrightarrow{+4} 10$)

Following this increasing difference pattern ($+2, +3, +4, \dots$), the next letter should be at position:

$$10 + 5 = 15 \implies \text{O}$$

2. Second Letter Pattern:

The second letters are $\text{D, G, K, P}$:

• $\text{D} \xrightarrow{+3} \text{G}$ (Positions: $4 \xrightarrow{+3} 7$)
• $\text{G} \xrightarrow{+4} \text{K}$ (Positions: $7 \xrightarrow{+4} 11$)
• $\text{K} \xrightarrow{+5} \text{P}$ (Positions: $11 \xrightarrow{+5} 16$)

Following this increasing difference pattern ($+3, +4, +5, \dots$), the next letter should be at position:

$$16 + 6 = 22 \implies \text{V}$$

Combining both letters, the next term in the sequence is OV.