In the mixed numeric–alphabetic pattern 1A2, 3C4, 7G8, ___, which of the following terms should come next to correctly extend the sequence?

Introduction / Context:
This question involves a hybrid series in which each term consists of a number, a letter and another number. Solving such problems requires simultaneously tracking how the numbers change from term to term and how the letters progress through the alphabet. The pattern here links the growth of the outer numbers and the shifts in the central letter in a systematic way.

Given Data / Assumptions:

• Known terms: 1A2, 3C4, 7G8, ___.
• Each term has the structure: number, letter, number.
• Exactly one term is missing, and must be chosen from the options.
• We assume that both the numeric parts and the letter part follow consistent rules.

Concept / Approach:
We split the problem into three related sequences: the first numbers (1, 3, 7, ?), the middle letters (A, C, G, ?), and the last numbers (2, 4, 8, ?). We then look for patterns in each. The numbers may grow by changing differences or by doubling; the letters may advance by skipping a fixed number of positions or by using the same step pattern as the outer numbers. Once these three subpatterns are identified, they must all point to the same candidate term.

Step-by-Step Solution:
Step 1: Analyse the first numbers: 1, 3, 7. Differences: 3 - 1 = 2, 7 - 3 = 4. Step 2: The increments themselves (2, 4) appear to double, suggesting the next increment should be 8. Step 3: So the next first number is 7 + 8 = 15. Step 4: Analyse the last numbers: 2, 4, 8. This is a simple doubling sequence: 2, 4, 8, so the next term is 8 * 2 = 16. Step 5: Now look at the middle letters: A, C, G. Positions: A = 1, C = 3, G = 7. Step 6: Differences: 3 - 1 = 2, 7 - 3 = 4, mirroring the first number differences. Step 7: The next increment should again be 8, so the next letter position is 7 + 8 = 15, which is O. Step 8: Combining these results, the missing term is 15O16.

Verification / Alternative check:
We can represent the pattern more compactly as a triple progression: the outer numbers follow 1, 3, 7, 15 (each time adding 2, 4, 8), while the inner letters correspond to positions 1, 3, 7, 15, and the final numbers are 2, 4, 8, 16 (successive doublings). All three components are driven by the same doubling rule for the increments, which gives a strong and elegant structural explanation.

Why Other Options Are Wrong:
16P17 does not match any of the three subpatterns: 16 is not the correct next first number, P(16) is one step beyond the correct letter O(15), and 17 is not a doubling of 8. Similarly, 14O15 and 13P14 either use partial aspects of the discovered pattern or none at all, but they fail to align all three parts simultaneously. Only 15O16 is consistent with every progression in the series.

Common Pitfalls:
Some students may focus on only one side of the term, such as the last numbers, and then guess the remaining parts. Others may overlook the fact that the differences between letter positions mirror the differences between the first numbers. Ignoring this connection can lead to plausible but incorrect guesses. Always cross check each component of the candidate term with all identified rules.

Final Answer:
The only option that continues the numerical and alphabetic patterns correctly is 15O16.