Analysis of the Series

To find the missing number, we need to identify the mathematical pattern governing the sequence: 336, 210, 120, 60, ___, 6.

One common approach is to look for a relationship with cubic numbers. The pattern can be described by the formula $n^3 - n$, where 'n' is a whole number that decreases with each step.

Applying the Pattern

Let's test this formula for the given terms:

• For n = 7: $7^3 - 7 = 343 - 7 = 336$
• For n = 6: $6^3 - 6 = 216 - 6 = 210$
• For n = 5: $5^3 - 5 = 125 - 5 = 120$
• For n = 4: $4^3 - 4 = 64 - 4 = 60$

Finding the Missing Term

The pattern holds, with 'n' decreasing by 1 for each term. The next term should correspond to n = 3.

For n = 3: $3^3 - 3 = 27 - 3 = 24$

To verify this, the final term in the series should correspond to n = 2:

For n = 2: $2^3 - 2 = 8 - 2 = 6$. This matches the last term.

Conclusion

The missing number in the series is 24.