Given Series

1. Given number series: 3, 7, 16, 35, 74, ?

Question

Find the next number in the given series.

Answer

153.

Solution

1. Analyze the transformation rule between successive terms:
2. 3 × 2 + 1 = 7
3. 7 × 2 + 2 = 16
4. 16 × 2 + 3 = 35
5. 35 × 2 + 4 = 74
6. Pattern rule: Multiply the previous term by 2 and add an increasing integer (+1, +2, +3, +4, +5).
7. Next term = 74 × 2 + 5 = 148 + 5 = 153.