Find the next term in the series 143, 143, 136, 110, ?.

Introduction / Context:
This number series question involves recognising a pattern in the differences between consecutive terms. The pattern is slightly non obvious, using values related to cubes, which makes this a moderately challenging mental maths problem.

Given Data / Assumptions:

• Series: 143, 143, 136, 110, ?
• Exactly one next term is required.
• The same rule governs all transitions between neighbouring terms.

Concept / Approach:
When the numbers do not appear to follow a simple multiplication pattern, the next step is to look at the differences between terms. If those differences themselves fit a clean formula, such as n^3 − 1 or a similar expression, we can extend that pattern to find the next difference and thus the missing term.

Step-by-Step Solution:
Step 1: Compute the differences: 143 − 143 = 0, 143 − 136 = 7, 136 − 110 = 26. Step 2: Consider the absolute values of the differences: 0, 7, 26. Notice that 0 = 1^3 − 1, 7 = 2^3 − 1, 26 = 3^3 − 1. Step 3: This suggests the pattern of subtracting successive numbers of the form n^3 − 1 where n increases by 1 each time: 1^3 − 1, 2^3 − 1, 3^3 − 1, 4^3 − 1, and so on. Step 4: The next difference should therefore be 4^3 − 1 = 64 − 1 = 63. Step 5: Subtract this difference from the last known term: 110 − 63 = 47.

Verification / Alternative check:
The completed series with the candidate term is 143, 143, 136, 110, 47. The absolute differences become 0, 7, 26, 63 which correspond to 1^3 − 1, 2^3 − 1, 3^3 − 1, 4^3 − 1. The pattern is consistent for each step, confirming that 47 is the correct next term.

Why Other Options Are Wrong:
Options 91, 35, and 69 produce differences that do not match the required cube minus one pattern. For example, if the term were 69, the last difference would be 110 − 69 = 41, which is not of the form n^3 − 1 for any integer n. Only 47 leads to the correct sequence of differences.

Common Pitfalls:
A common mistake is to look for simple linear or geometric patterns and give up when they are not found. Another error is to ignore the absolute value of the first difference, which here neatly fits the same formula as the others. When dealing with unusual series, always test for relationships involving squares or cubes of small integers.

Final Answer:
The next term in the series following the cube minus one pattern is 47.