Number series – find the next two terms: 28, 25, 5, 21, 18, 5, 14, ?, ?

Introduction / Context:
This sequence mixes a small constant decrement with two alternating adjustments whose magnitudes reduce in a steady pattern. We must project the rule two more steps to find the next pair.

Given Data / Assumptions:

• Series (spaces imply commas): 28, 25, 5, 21, 18, 5, 14, ?, ?
• We want terms 8 and 9.
• Observed differences: -3, -20, +16, -3, -13, +9, -3, …

Concept / Approach:

Notice a repeating three-step motif: subtract 3, subtract a larger value, then add a value. The larger subtraction and the addition each decrease by 7 on successive cycles.

Step-by-Step Solution:

Verification / Alternative check:

Projecting further with +2 would give 7, consistent with the established 16 → 9 → 2 trend in the additive leg.

Why Other Options Are Wrong:

10 7, 11 8, 5 10, 10 5 do not align with the strictly “−3, then (−7 less than previous large subtraction), then (+7 less than previous addition)” pattern.

Common Pitfalls:

Assuming a single arithmetic progression or alternating parity sequences fails because the sequence uses a three-step cyclic difference pattern.

Final Answer:

11 5