Number Series — Multiply by 3 and Subtract 2 Rule Find the missing number in the sequence: 4, 10, ?, 82, 244, 730

Introduction / Context:
Some sequences use a fixed two-step operation: multiply by a constant and then add or subtract a small constant. Spotting these paired operations yields quick answers.

Given Data / Assumptions:

• Sequence: 4, 10, ?, 82, 244, 730
• We suspect a repeated operation of the form: next = current * 3 − 2.

Concept / Approach:
Verify the rule between known adjacent terms. If 82 = 28 * 3 − 2 and 244 = 82 * 3 − 2, then the missing term before 82 should be 28, and the whole sequence stays consistent.

Step-by-Step Solution:
Check initial step: 4 * 3 − 2 = 12 − 2 = 10 ✔Find the missing term x: x * 3 − 2 = 82 ⇒ x * 3 = 84 ⇒ x = 28Continue: 82 * 3 − 2 = 246 − 2 = 244 ✔Next: 244 * 3 − 2 = 732 − 2 = 730 ✔

Verification / Alternative check:
All transitions align perfectly with ‘‘multiply by 3 then subtract 2’’. Hence, the only value that preserves the rule at the missing position is 28.

Why Other Options Are Wrong:

• 24, 77, 218: Substituting any of these will not yield 82 after applying *3 − 2.

Common Pitfalls:
Trying additive differences in strongly multiplicative growth sequences. Always test a simple multiply-then-adjust rule first in such contexts.

Final Answer:
28