Number Series Analysis

The series provided is 4, 6, 8, 18, 16, ? . We need to determine the number that should replace the question mark.

Interleaved Sequences

The series follows a pattern involving two separate sequences interleaved:

• Odd-indexed terms: 4, 8, 16
• Even-indexed terms: 6, 18, ?

Odd Position Terms: Geometric Progression

Consider the terms at odd positions: 4, 8, 16.

This sequence follows a geometric progression where each term is multiplied by 2 to get the next term:

$4 \times 2 = 8$

$8 \times 2 = 16$

Even Position Terms: Multiplication Pattern

Now, look at the terms at even positions: 6, 18, ?.

The pattern here involves multiplying the previous term by 3:

$6 \times 3 = 18$

Calculating the Next Term

To find the missing term (which is at the 6th position), we apply the same multiplication pattern (by 3) to the preceding even-indexed term (18):

$18 \times 3 = 54$

Solution Value

Therefore, the number 54 replaces the question mark.