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

CONCEPT

A recursive number series can combine multiplication with an added sequence. To identify the rule, compare each term with a fixed multiple of the preceding term and inspect the residuals.

APPLICATION

1. From 1 to 6: 2 × 1 + 4 = 6.

2. From 6 to 18: 2 × 6 + 6 = 18.

3. From 18 to 44: 2 × 18 + 8 = 44.

4. From 44 to 98: 2 × 44 + 10 = 98.

5. From 98 to 208: 2 × 98 + 12 = 208.

6. From 208 to 430: 2 × 208 + 14 = 430.

7. The added even numbers increase by 2, so the next one is 16: 2 × 430 + 16 = 876.

CROSS-CHECK

The residuals after subtracting twice the preceding term are 4, 6, 8, 10, 12, 14 and 16, a consecutive-even-number sequence.

Therefore, the missing number is 876.