Find the number that can replace question mark (?) in the series given below:…

Concept

A number series may be generated by applying a fixed operation and a changing adjustment to each term. The operation and the adjustment pattern must account for every adjacent pair.

Here, each term is multiplied by 3, while the added number increases by 1 at each step.

Application

1. 20 × 3 + 2 = 62.

2. 62 × 3 + 3 = 189.

3. 189 × 3 + 4 = 571.

4. 571 × 3 + 5 = 1718.

5. The next added number is 6, so 1718 × 3 + 6 = 5154 + 6 = 5160.

Cross-check

Reversing the last step gives (5160 − 6) ÷ 3 = 1718. The successive added numbers are 2, 3, 4, 5, 6, so the continuation is consistent.

Therefore, the required number is 5160.