Number series — choose the next term. Sequence: 11, 13, 17, 19, 23, 25, ?

Introduction / Context: The sequence alternates between adding 2 and adding 4, a common construction that mostly tracks prime-like steps but includes a non-prime deliberately to cue attention to the step sizes rather than primality.

Given Data / Assumptions:

• Terms: 11, 13, 17, 19, 23, 25, ?
• We focus on differences, not on primality alone (since 25 is not prime).

Concept / Approach: Compute successive differences: 13 − 11 = 2; 17 − 13 = 4; 19 − 17 = 2; 23 − 19 = 4; 25 − 23 = 2. The pattern clearly alternates +2, +4, +2, +4, +2, so the next difference should be +4.

Step-by-Step Solution: Apply the alternating increment: after +2 to reach 25, next add +4. Next term = 25 + 4 = 29. Check continuity across all terms to ensure the alternation is unbroken.

Verification / Alternative check: Reconstructing: 11 (+2) 13 (+4) 17 (+2) 19 (+4) 23 (+2) 25 (+4) 29 confirms the pattern.

Why Other Options Are Wrong: 26/27/37: Do not equal 25 + 4; they would violate the +2/+4 alternation.

Common Pitfalls: Assuming “next prime” after 23 and being confused by 25; the rule is increments, not primality.

Final Answer: 29