A letter series is given with one term missing: CAR, GCO, KEL, OGI, ?. Which of the following three letter groups should replace the question mark to continue the alphabetic pattern correctly?

Introduction / Context:
This question presents a three letter alphabet series: CAR, GCO, KEL, OGI, and a missing term. The task is to determine which three letter group completes the series in a logical manner. This type of question assesses the ability to recognise combined patterns involving positive and negative shifts in letter positions in the English alphabet.

Given Data / Assumptions:

• Known terms: CAR, GCO, KEL, OGI.
• Each term contains exactly three letters.
• The pattern may involve different step sizes for each position within the three letter group.
• Alphabet positions: A is 1, B is 2, and so on up to Z as 26.
• Options: SIK, SIF, TIK, TIL.

Concept / Approach:
To find the pattern, we convert each letter into its numerical position and examine the changes in the first, second, and third letters separately from term to term. It is common for such series to involve different increments or decrements for each position. After observing a consistent pattern, we apply it to the latest term to deduce the missing group.

Step-by-Step Solution:
Step 1: Convert CAR to numerical positions: C(3), A(1), R(18).Step 2: Convert GCO: G(7), C(3), O(15).Step 3: Convert KEL: K(11), E(5), L(12).Step 4: Convert OGI: O(15), G(7), I(9).Step 5: Observe the first letters: C(3) to G(7) is +4, G(7) to K(11) is +4, and K(11) to O(15) is also +4. Hence the first letter increases by 4 each time.Step 6: Observe the second letters: A(1) to C(3) is +2, C(3) to E(5) is +2, and E(5) to G(7) is +2. Thus, the second letter increases by 2 each step.Step 7: Observe the third letters: R(18) to O(15) is -3, O(15) to L(12) is -3, and L(12) to I(9) is also -3. So the third letter decreases by 3 each time.Step 8: Apply these rules to OGI: first letter O(15) plus 4 gives 19, which is S. Second letter G(7) plus 2 gives 9, which is I. Third letter I(9) minus 3 gives 6, which is F.Step 9: The next term must therefore be SIF.

Verification / Alternative check:
Placing SIF into the sequence gives a consistent pattern: first letters C, G, K, O, S all differ by +4; second letters A, C, E, G, I by +2; and third letters R, O, L, I, F by -3. No other option matches all three transformation rules simultaneously, so SIF is uniquely correct.

Why Other Options Are Wrong:
SIK, TIK, and TIL may match some positions partially but fail when the exact increments are checked. For example, TIK would require a first letter change of +5 from O to T, which violates the established +4 rule. Therefore, they cannot be accepted as valid continuations of the series.

Common Pitfalls:
A frequent mistake is to focus only on one position, such as the first letters, and ignore the remaining positions. Another pitfall is to guess based on visual similarity rather than verifying the numeric differences. A methodical check of all three positions is essential in series of this type.

Final Answer:
The correct group of letters that completes the series is SIF.