Number series — find the next two terms. Sequence: 2, 15, 4, 12, 6, 7, ?, ?

Introduction / Context:
This is a number-series question that tests pattern recognition with interleaved (alternating) subsequences. Many competitive exams hide two simpler progressions inside a single list. Spotting and separating those strands is the key skill being assessed.

Given Data / Assumptions:

• Given sequence: 2, 15, 4, 12, 6, 7, ?, ?
• We assume a deterministic numeric pattern without external data.
• We consider the possibility of two alternating subsequences (odd/even positions).

Concept / Approach:
Split the sequence into terms at odd and even positions to see if each forms a simpler rule. Odd positions: 1st, 3rd, 5th, 7th. Even positions: 2nd, 4th, 6th, 8th. Look for simple arithmetic changes such as constant addition/subtraction steps or small linear rules.

Step-by-Step Solution:
Odd-position terms: 2 (1st), 4 (3rd), 6 (5th), ? (7th). Pattern is +2 each step, so the 7th term = 6 + 2 = 8. Even-position terms: 15 (2nd), 12 (4th), 7 (6th), ? (8th). Differences are −3 then −5; a common progression here is subtracting consecutive odd numbers: −3, −5, next −7. Compute 8th term: 7 − 7 = 0.

Verification / Alternative check:
Rebuild the full sequence with the derived terms: 2, 15, 4, 12, 6, 7, 8, 0. Each subsequence consistently follows its rule (+2 for odds, −3/−5/−7 for evens).

Why Other Options Are Wrong:
8, 8: Correct 7th term but ignores the even-position decreasing pattern. 3, 8: Breaks the steady +2 rule in the odd positions. None of these: Not applicable since 8, 0 fits perfectly.

Common Pitfalls:
Mixing positions or trying to force a single-step rule across all terms rather than splitting into alternating strands.

Final Answer:
8, 0