Number series (find the next two terms): 10 34 12 31 14 28 16 Choose the pair that correctly completes the sequence.

Introduction / Context:
This series interleaves two independent arithmetic progressions, one increasing and one decreasing. Such paired sequences are routine in aptitude exams.

Given Data / Assumptions:

• Sequence: 10, 34, 12, 31, 14, 28, 16, ? , ?
• Two end terms are missing.

Concept / Approach:
Split by position: Odd-index terms and even-index terms. Compute each pattern separately.

Step-by-Step Solution:
Odd positions (1st, 3rd, 5th, 7th): 10, 12, 14, 16 → increment +2 each time; next odd (9th) will be 18.Even positions (2nd, 4th, 6th): 34, 31, 28 → decrement −3; next even (8th) will be 25.Hence the next two numbers (8th then 9th) are 25 and 18.

Verification / Alternative check:
List the two progressions: Even: 34, 31, 28, 25; Odd: 10, 12, 14, 16, 18. Interleaving confirms the answer 25 18.

Why Other Options Are Wrong:

• 30 13 / 19 26 / 18 20 / 25 22: Each breaks either the −3 even term rule or the +2 odd term rule.

Common Pitfalls:
Ignoring position-based splitting; without it the numbers look erratic.

Final Answer:
25 18