Understanding the Sequence Pattern Question

This question asks us to find a missing element in a given expression by observing the pattern in a longer sequence provided. We need to carefully examine the relationship between the elements present in the expression and their positions within the original sequence.

Analyzing the Given Sequence and Expression

The original sequence is: ABC$+#DEF&=?GHI!2*@

Let's list the elements and their positions in this sequence:

The expression with the blank is: A $ D _____ G ! @

Let's find the positions of the known elements from the expression in the original sequence:

• A is at position 1
• $ is at position 4
• D is at position 7
• G is at position 13
• ! is at position 16
• @ is at position 19

So, the sequence of positions in the expression is: 1, 4, 7, _____, 13, 16, 19.

(Note: There was a slight typo in the original sequence definition provided in the question body vs the expression itself. The '@' in the sequence seems to be at position 19 based on counting, while the expression lists it last. We will use the sequence as the source of elements and positions: `ABC$+#DEF&=?GHI!2*@` - this sequence is 19 characters long, not 20. Let's recount positions based on this 19-character sequence carefully.)

Corrected sequence and positions:

Using the 19-character sequence ABC$+#DEF&=?GHI!2*@:

• A is at position 1
• $ is at position 4
• D is at position 7
• G is at position 13
• ! is at position 16
• @ is at position 19

The positions in the expression are: 1, 4, 7, _____, 13, 16, 19.

Finding the Pattern: Positions and Skips

Let's look at the difference in positions between consecutive elements in the expression:

• From A (pos 1) to $ (pos 4): $\text{4 - 1 = 3}$
• From $ (pos 4) to D (pos 7): $\text{7 - 4 = 3}$
• From D (pos 7) to the missing element (pos X): $\text{X - 7 = Y1}$
• From the missing element (pos X) to G (pos 13): $\text{13 - X = Y2}$ (where $\text{Y1 + Y2 = 13 - 7 = 6}$)
• From G (pos 13) to ! (pos 16): $\text{16 - 13 = 3}$
• From ! (pos 16) to @ (pos 19): $\text{19 - 16 = 3}$

Looking at the differences, we see a pattern of '3' between most elements: 3, 3, Y1, Y2, 3, 3. It seems highly likely that the pattern is consistently adding 3 to the position to get the next element's position in the expression, at least up to the missing element and possibly afterwards.

Let's assume the difference is 3 between D and the missing element.

• Position of missing element = Position of D + 3 = 7 + 3 = 10.

So, the missing element is at position 10 in the original sequence.

Identifying the Missing Element

Based on our corrected sequence ABC$+#DEF&=?GHI!2*@, the element at position 10 is &.

Verifying the Pattern

If the missing element is & (at position 10), the sequence of positions in the expression becomes: 1, 4, 7, 10, 13, 16, 19.

Let's check the differences:

• 4 - 1 = 3
• 7 - 4 = 3
• 10 - 7 = 3
• 13 - 10 = 3
• 16 - 13 = 3
• 19 - 16 = 3

The pattern of adding 3 to the position is consistent throughout the entire expression when the element at position 10 (&) is placed in the blank.

Alternatively, we can describe the pattern as taking an element from the original sequence and then skipping two elements to get the next element in the expression:

• A (pos 1) -> Skip B, C (2 elements) -> $ (pos 4)
• $ (pos 4) -> Skip +, # (2 elements) -> D (pos 7)
• D (pos 7) -> Skip E, F (2 elements) -> & (pos 10)
• & (pos 10) -> Skip =, ? (2 elements) -> G (pos 13)
• G (pos 13) -> Skip H, I (2 elements) -> ! (pos 16)
• ! (pos 16) -> Skip 2, * (2 elements) -> @ (pos 19)

This pattern of skipping exactly 2 elements between consecutive terms in the expression is also perfectly consistent when & is the missing element.

Conclusion

Both methods of analyzing the pattern (position differences and elements skipped) point to the element at position 10 in the original sequence as the missing element. The element at position 10 is &.

Comparing this with the given options, the element & corresponds to option 1.

Revision Table: Sequence Pattern Analysis

Additional Information: Logical Reasoning and Sequence Puzzles

Sequence and pattern questions are common in logical reasoning and aptitude tests. They require careful observation to identify the underlying rule or pattern governing the series of elements. Patterns can be based on:

• Position in the original list or alphabet/numbers.
• Differences or ratios between consecutive terms (for numerical sequences).
• Skipping a fixed number of elements.
• Alternating patterns or combined patterns.
• Properties of the elements themselves (e.g., vowels, consonants, symbols).

Solving these puzzles involves breaking down the sequence, testing potential patterns, and verifying the identified pattern across the entire sequence or expression.