Select the number from among the given options that can replace the question…

Many number series follow a linear recurrence: each term equals the previous term multiplied by a fixed constant, then adjusted by a fixed addition or subtraction. To crack such a series, first check whether the ratio between consecutive terms is roughly steady, then find the small correction that makes the ratio exact.

1. Check the ratio between successive terms: 18 ÷ 5 = 3.6, 70 ÷ 18 ≈ 3.89, 278 ÷ 70 ≈ 3.97 — the ratio keeps rising toward 4, pointing to a multiplier of 4 with a small correction.

2. Test the rule "previous term × 4, minus a constant": 5 × 4 = 20 and 20 − 18 = 2; 18 × 4 = 72 and 72 − 70 = 2; 70 × 4 = 280 and 280 − 278 = 2. Every consecutive pair gives the same correction of 2, confirming the rule: next term = (previous term × 4) − 2.

3. Apply the confirmed rule to the last given term: 278 × 4 = 1112, and 1112 − 2 = 1110.

Reversing the operation on 1110 gives (1110 + 2) ÷ 4 = 1112 ÷ 4 = 278, which matches the given term exactly, confirming both the rule and the missing number.