Identify the missing term in the following number series:
$$5,6,18,9,21,3,24,?$$

The given series is an alternating series containing two interleaved patterns:
Pattern 1 (Odd-indexed positions: 1st, 3rd, 5th, 7th...):

$$5,18,21,24$$

Let's look at the relation from the 3rd term onwards:

* $18+3=21$
* $21+3=24$
(Note: 5 is a starting seed value or part of a different sub-relation, but the operational pattern logic works precisely with Pattern 2).

Pattern 2 (Even-indexed positions: 2nd, 4th, 6th, 8th...):

$$6,9,3,?$$

Let's observe the mathematical relationship between the successive pairs of numbers across the combined sequence:

* ${\text{Term}}_1=5$
* ${\text{Term}}_2=5+1=6$
* ${\text{Term}}_3=6\times 3=18$
* ${\text{Term}}_4=18÷2=9$
* ${\text{Term}}_5=9+12=21$
* ${\text{Term}}_6=21÷7=3$
* ${\text{Term}}_7=3\times 8=24$

Alternatively, looking purely at the operations to get the next numbers:
Instead, notice the triplets structure:

* $(5\times 3)+3=18\to$ not matching.

Let's look at the exact step differences:

1. $5\to 6(+1)$
2. $6\to 18(\times 3)$
3. $18\to 9(-9\text{ or }÷2)$
4. $9\to 21(+12)$
5. $21\to 3(-18\text{ or }÷7)$
6. $3\to 24(\times 8)$

Let's check the alternative standard alternate series rule:
Terms at even positions: $6,9,3,?$
Notice that for each pair of odd and even terms:

* ${\text{Term}}_2={\text{Term}}_1+1⟹5+1=6$
* ${\text{Term}}_4={\text{Term}}_3÷2⟹18÷2=9$
* ${\text{Term}}_6={\text{Term}}_5÷7⟹21÷7=3$

Following this logic for the next pair (${\text{Term}}_7$ and ${\text{Term}}_8$):
Notice the operations used to derive even terms from odd terms are $+1$, $÷2$, $÷7$. Let's look closely at the alternate logic:

$$6\stackrel{+3}{\to }9\stackrel{-6}{\to }3\stackrel{+3}{\to }6$$

The pattern at even places is $+3,-6,+3,-6\dots$

* $6+3=9$
* $9-6=3$
* $3+3=6$

Let's verify the odd positions with this logic:

$$5\stackrel{+13}{\to }18\stackrel{+3}{\to }21\stackrel{+3}{\to }24$$

Thus, the missing term at the 8th position (even place) must be $3+3=6$.