Subsequent terms in all the given three number series should follow the pattern “1 more than the square of consecutive odd numbers” .

A: 32, 82, 164, 286, 456, 682

B: 140, 166, 216, 338, 508, 798

C: 400, 410, 435, 485, 567, 689

Which of the following series does not follow the pattern?

The correct option is Both B and C.

To determine which series does not follow the given pattern, we need to analyze the differences between consecutive terms in each series. According to the problem statement, these differences must follow the pattern of "1 more than the square of consecutive odd numbers".

Mathematically, the difference between consecutive terms should be of the form:

$d=n^2+1$

where $n$ represents consecutive odd numbers (e.g., 3, 5, 7, 9, 11, ...).

Let us analyze each series one by one:

Analysis of Series A: 32, 82, 164, 286, 456, 682
Calculating the differences between consecutive terms:
- First difference: $82-32=50$, which is $7^2+1$ (odd number 7)
- Second difference: $164-82=82$, which is $9^2+1$ (odd number 9)
- Third difference: $286-164=122$, which is ${11}^2+1$ (odd number 11)
- Fourth difference: $456-286=170$, which is ${13}^2+1$ (odd number 13)
- Fifth difference: $682-456=226$, which is ${15}^2+1$ (odd number 15)
Since the differences follow the pattern for consecutive odd numbers (7, 9, 11, 13, 15), Series A follows the pattern.

Analysis of Series B: 140, 166, 216, 338, 508, 798
Calculating the differences between consecutive terms:
- First difference: $166-140=26$, which is $5^2+1$ (odd number 5)
- Second difference: $216-166=50$, which is $7^2+1$ (odd number 7)
- Third difference: $338-216=122$, which is ${11}^2+1$ (odd number 11)
Here, the difference of $9^2+1=82$ is missing between 216 and 338. Therefore, Series B does not follow the pattern.

Analysis of Series C: 400, 410, 435, 485, 567, 689
Calculating the differences between consecutive terms:
- First difference: $410-400=10$, which is $3^2+1$ (odd number 3)
- Second difference: $435-410=25$
The expected second difference should be $5^2+1=26$. Since the actual difference is 25, Series C does not follow the pattern.

Thus, both Series B and Series C do not follow the prescribed pattern.