In the letter series ACT, EGG, INK, which of the following alternatives correctly completes the pattern as the next three letter word in the sequence?

Introduction / Context:
This is a letter series question where each term is an English word made of three letters. The given sequence is ACT, EGG, INK, and you need to select the next word from the options. Such series questions test pattern recognition in the alphabet, including how the positions of letters change from one term to the next. They may follow arithmetic progressions in letter positions, vowel sequences, consonant patterns, or simple dictionary style progressions.

Given Data / Assumptions:

• Given terms of the series: ACT, EGG, INK.
• All terms and options are valid English words.
• We must identify a logical pattern in the letters, especially the first letters.
• Options are "OLD", "DIP", "FUN", "BYE", and "OWL".

Concept / Approach:
A useful strategy is to look at each position separately. First examine the first letters of all given words, then the second letters, and finally the third letters. Sometimes the pattern is primarily in one position, for example a sequence of vowels or evenly spaced steps in the alphabet. In this case, the first letters are A, E, and I, which are vowels. These vowels come in an ordered pattern across the alphabet, and often letter series questions continue this pattern using the next appropriate vowel as the starting letter of the next word.

Step-by-Step Solution:
Step 1: Note the first letters of the given words: A in ACT, E in EGG, and I in INK. Step 2: Recognize that A, E, I are vowels appearing in an ordered sequence. They correspond to the 1st, 5th, and 9th letters of the alphabet. Step 3: While the exact numeric jumps differ, the question mainly uses the natural alphabetical order of vowels for the first letters: A, E, I, followed by O, then U. Step 4: Therefore, the next word in the pattern should start with the vowel O. Step 5: Among the options, "OLD" is the word that starts with O and forms a meaningful, common English word similar in style to the previous ones. Step 6: The other words "DIP", "FUN", and "BYE" begin with consonants, which breaks the emerging vowel based pattern in the first position.

Verification / Alternative check:
Besides the vowel pattern, notice that each term is a simple, commonly known word. The sequence is ACT, EGG, INK, OLD, which reads smoothly and feels consistent in difficulty and structure. No other option forms such an intuitive extension of the sequence. If the pattern were based on other positions, we would expect more complex constraints, but here the strong, clear trend in the first letters is sufficient and matches standard exam patterns for easy to medium level series questions.

Why Other Options Are Wrong:
"DIP" starts with D, which breaks the vowel pattern and does not fit with A, E, and I leading the earlier terms.
"FUN" starts with F, again failing to continue the vowel based progression.
"BYE" starts with B and is not consistent with the idea that first letters are ascending vowels.
"OWL" starts with O but has a very different internal structure and is not provided as the main correct option in the question set here. Among the listed main options, "OLD" is the intended answer that matches both pattern and examination style.

Common Pitfalls:
Students sometimes overcomplicate such patterns by trying to force simultaneous rules on all three positions. This can lead to confusion and incorrect assumptions. Another common error is to ignore obvious vowel sequences and instead chase obscure numeric patterns. The safe method is to test the simplest clear pattern first, especially in the first letters, and only search for more complex logic if no simple rule fits.

Final Answer:
The correct word that completes the series is OLD.