Look at this series: 8, 6, 9, 23, 87, ... What number should come next?

Given data

• Terms: 8, 6, 9, 23, 87, ...

Concept/ApproachThe recursive rule follows an increasing multiplier with a concurrent linear subtraction: multiply by n and subtract (n + 1), where n starts at 1 for the move from the first term.

Step-by-step calculation8 × 1 − 2 = 66 × 2 − 3 = 99 × 3 − 4 = 2323 × 4 − 5 = 87Next uses n = 5: 87 × 5 − 6 = 435 − 6 = 429

Verification/AlternativeThe pattern '×n then −(n+1)' consistently reproduces every given transition; extending it yields 429.

Common pitfalls

• Searching for fixed differences or ratios; neither is constant here.
• Assuming alternating add/subtract without the multiplicative growth.

Final Answer429