Number Series — Multiplicative Pattern with Increment Find the next number in the sequence: 3, 7, 23, 95, ?

Introduction / Context:Series can grow rapidly due to multiplicative rules combined with small additive increments. Identifying the correct multiplier and incremental add-on is key for quick solutions in exams.

Given Data / Assumptions:

• Given series: 3, 7, 23, 95, ?
• We suspect a pattern of the form: next = current * k + c, where k and c may vary.

Concept / Approach:Check transitions term by term to see if there is a systematic increase in multiplier and a small, related add-on. A common construction is multiplying by consecutive integers and then adding a steadily increasing small number.

Step-by-Step Solution:3 → 7: 3 * 2 + 1 = 77 → 23: 7 * 3 + 2 = 2323 → 95: 23 * 4 + 3 = 95Pattern: multiply by 2, 3, 4, and add 1, 2, 3 respectively.Next step should be: multiply by 5 and add 4.95 * 5 + 4 = 475 + 4 = 479

Verification / Alternative check:The sequence rule is consistent across all transitions: multiplier increases by 1 and the added constant also increases by 1. Thus, 479 follows logically.

Why Other Options Are Wrong:

• 62, 128, 575: These do not satisfy the established rule of *5 then +4 from 95.

Common Pitfalls:Assuming a constant multiplier or skipping the additive pattern. Always test a few transitions to reveal both parts of the rule.

Final Answer:479