In the sequence 101, 98, 93, 86, 75, ?, find the next number that continues the pattern.

Introduction / Context:
This series is strictly decreasing, and the drops between terms are not constant. Many such sequences are based on subtracting successive prime numbers or odd numbers. Identifying that pattern is the key to finding the next term.

Given Data / Assumptions:

• Series: 101, 98, 93, 86, 75, ?
• The terms are decreasing.
• We assume there is a single clean rule based on subtraction.

Concept / Approach:
When a sequence is decreasing with irregular steps, we usually investigate whether the differences correspond to a familiar sequence such as prime numbers, odd numbers or multiples of a constant. Once we see a familiar pattern, we extend it to calculate the next difference and therefore the next term.

Step-by-Step Solution:
Step 1: Calculate the differences: 101 - 98 = 3, 98 - 93 = 5, 93 - 86 = 7, 86 - 75 = 11.Step 2: The differences are 3, 5, 7 and 11.Step 3: These are prime numbers, but not starting from 2. The visible primes here are 3, 5, 7 and 11.Step 4: The next prime number after 11 is 13.Step 5: Subtract 13 from the last term: 75 - 13 = 62.

Verification / Alternative check:
Listing the primes in order: 2, 3, 5, 7, 11, 13 and so on. The sequence uses 3, 5, 7 and 11. Even though 2 is skipped, the pattern after that is consistent, so using 13 next is natural. If we use any other subtraction value, such as 12 or 14, the pattern ceases to align with prime numbers.

Why Other Options Are Wrong:
Values such as 68, 71 or 73 correspond to subtracting 7, 4 or 2 from 75, which does not follow the prime sequence after 11. Only 62 is obtained by subtracting 13, the next prime after 11, so the alternatives must be rejected.

Common Pitfalls:
Learners sometimes look for differences that increase by a constant amount, which does not work here. Another pitfall is assuming that the series must start with the very first prime, whereas exam questions may start from a prime in the middle of the list. Focusing on the visible pattern rather than expectations is essential.

Final Answer:
The next term in the series, obtained by subtracting the next prime number 13 from 75, is 62.