In the number series 6859, 5832, ?, 4096, 3375, a single term is missing. Choose the number that should replace the question mark.

Introduction / Context:
The series 6859, 5832, ?, 4096, 3375 clearly contains large numbers that are close to perfect cubes. Recognition of such forms is vital in reasoning tests, because many sequences are simply a list of cubes in increasing or decreasing order. Our aim is to identify the missing cube in this descending series.

Given Data / Assumptions:

• Series: 6859, 5832, ?, 4096, 3375.
• Exactly one term is missing.
• Numbers appear to be cubes of integers.

Concept / Approach:
We test each known term to see whether it matches n^3 for some integer n and then check whether the sequence of n values follows a simple pattern such as consecutive integers. Once we know the pattern of cube roots, the missing term is straightforward to determine.

Step-by-Step Solution:
1. Test the first term 6859. 2. 19^2 = 361 and 19^3 = 19 * 361 = 6859, so 6859 = 19^3. 3. Test the second term 5832. 4. 18^3 = 18 * 18 * 18 = 5832, so 5832 = 18^3. 5. The fourth term 4096 is 16^3, since 16^2 = 256 and 256 * 16 = 4096. 6. The fifth term 3375 is 15^3, since 15 * 15 * 15 = 3375. 7. So the cube roots we see are 19, 18, ?, 16, 15 forming a descending sequence. 8. The missing cube should correspond to 17^3. 9. Compute 17^3: 17^2 = 289 and 289 * 17 = 4913. 10. Therefore the missing term is 4913.

Verification / Alternative check:
Rebuild the complete series using cube values: 19^3 = 6859, 18^3 = 5832, 17^3 = 4913, 16^3 = 4096, 15^3 = 3375. The cube roots follow 19, 18, 17, 16, 15, which is a simple descending sequence of consecutive integers.

Why Other Options Are Wrong:

• 4589, 5013, 5169: None of these are perfect cubes of integers between 18 and 16. They do not fit the clean pattern of consecutive cubes.

Common Pitfalls:
Sometimes candidates try to find patterns in differences, which are complex for cube based series. Recognising perfect cubes is much faster, especially when the numbers are of the approximate size of n^3 for small n between 10 and 20.

Final Answer:
The missing number in the series is 4913.