What number would replace question mark (?) in the series given below? 1, 6,…

Concept

In a recurrence series, a term may be generated from the two preceding terms.

A valid rule must reproduce every known term before it is used to calculate the missing term.

Application

1. Test the rule: current term = 2 × (preceding term + the term before it).

2. The third term is 2 × (6 + 1) = 14.

3. The fourth term is 2 × (14 + 6) = 40.

4. The fifth term is 2 × (40 + 14) = 108.

5. The sixth term is 2 × (108 + 40) = 296.

6. The seventh term is 2 × (296 + 108) = 808.

7. The eighth term is 2 × (808 + 296) = 2 × 1104 = 2208.

Cross-check

Reverse the same relation: 2208 ÷ 2 − 808 = 296, which recovers the term two places before the missing term.

Therefore, the missing number is 2208.