Number series (find the next two terms): 17 32 19 29 21 26 23 Choose the pair that correctly completes the sequence.

Introduction / Context:
This is a classic two-interleaved-arithmetic-series problem frequently seen in reasoning tests. One subsequence is increasing while the other is decreasing. We must identify the pattern and then supply the next two terms.

Given Data / Assumptions:

• Observed sequence: 17, 32, 19, 29, 21, 26, 23, ? , ?
• Exactly two consecutive terms are missing at the end.
• Only one logical pattern should govern the entire sequence.

Concept / Approach:
Split the sequence by odd and even positions (1-indexed): the odd-position terms form one arithmetic progression; the even-position terms form another. Then compute each trend independently.

Step-by-Step Solution:
Odd positions: 1st=17, 3rd=19, 5th=21, 7th=23 → each step +2. So the 9th term should be 25.Even positions: 2nd=32, 4th=29, 6th=26 → each step −3. So the 8th term should be 23.Therefore, the next two terms (8th and 9th) are 23 and 25 respectively.

Verification / Alternative check:
Write the two progressions explicitly: even-index series 32, 29, 26, 23 (−3 each time) and odd-index series 17, 19, 21, 23, 25 (+2 each time). Merging them preserves the given order.

Why Other Options Are Wrong:

• 25 25 / 25 22 / 27 32 / 20 22: Each breaks either the −3 rule for even positions or the +2 rule for odd positions.

Common Pitfalls:
Looking for a single-step rule across all numbers rather than separating into interleaved subsequences often obscures the simple arithmetic patterns.

Final Answer:
23 25