Select the number from among the given options that can replace the question mark (?) in the following series.
4,10,23,67,137,?

Let's find the step differences between the terms:
10−4=6

23−10=13

67−23=44

137−67=70

Let's look closely at the alternating patterns or standard multiplier rules for the series directly:

4×2+2=10

10×2+3=23

23×3−2=67

67×2+3=137

Wow! Look at this alternating multiplier rule:

Term 1 to Term 2: ×2+2

Term 2 to Term 3: ×2+3

Term 3 to Term 4: ×3−2 (Wait, let's look for a clearer pattern)

Let's recheck:

4×3−2=10

10×2+3=23

23×3−2=67

67×2+3=137

The pattern is perfectly alternating between:

(Term×3)−2

(Term×2)+3

Let's trace it carefully:

4×3−2=12−2=10

10×2+3=20+3=23

23×3−2=69−2=67

67×2+3=134+3=137

Following this logic, the next operation must be (Term×3)−2:

137×3−2=411−2=409