Explanation:

Correct Option 4: Both Y and Z
Analyze Number Series Patterns
The given pattern is "1 more than the square of a consecutive odd number". This means the numbers following this pattern are of the form n² + 1, where n is a consecutive odd number (e.g., 1, 3, 5, 7, 9,...).
The phrasing suggests that the pattern applies to how subsequent terms are generated. Based on the numbers, it is highly probable that the differences between consecutive terms follow this pattern.
Let's list the values of n² + 1 for consecutive odd numbers starting from n = 1:
• For n = 1,1²+1=1+1=2
• For n=3,3²+1=9+1=10
• For n=5,5²+1=25+1=26
• For n=7,7²+1=49+1=50
• For n = 9,9²+1 = 81+1 = 82
• For n = 11,11² + 1 = 121 + 1 = 122
• For n = 13,13² + 1 = 169 +1 = 170
• For n= 15, 15²+1=225+1 = 226
• For n = 17,17² +1=289+1=290
The sequence of pattern values is 2, 10, 26, 50, 82, 122, 170, 226, 290, ... Analyzing Series X
Series X is: 66, 148, 270, 440,666, 956
Let's find the differences between consecutive terms:
• 148 - 66  =  82
• 270 - 148  = 122
• 440-270  = 170
• 666 - 440 = 226
• 956-666 = 290
The differences are: 82, 122, 170, 226,290.
Let's compare these differences with the pattern values n² + 1:
·82= 9²+1 (Here n = 9)
122= 11^{2 +} 1 (Here n = 11)
170 = 13² + 1 (Here n = 13)
226 = 15² +1 (Here n = 15)
290 = 17² +1 (Here n = 17)
The differences are n² + 1 where n takes consecutive odd values (9, 11, 13, 15, 17). Therefore, Series X follows the specified pattern.
Analyzing Series Y
Series Y is: 138, 148, 174, 224, 346, 516
Let's find the differences between consecutive terms:
•  148 - 138 = 10
• 174 -148 =  26
• 224 - 174 = 50
.•  346 - 224 =122
• 516 -  346 = 170
The differences are: 10, 26, 50, 122, 170.
Let's compare these differences with the pattern values n² + 1:
10=3²  + 1 (Here n = 3)
26= 5²+1 (Here n = 5)
.50=7² +1 (Here n = 7)
122 = 11²+1 (Here n = 11)
170 = 13²  + 1 (Here n = 13)
The differences are of the form n²+1, but the values of n are 3, 5, 7, 11, 13. This sequence of odd numbers (3, 5, 7, 11, 13) is not consecutive as it skips the odd number 9. Therefore, Series Y does not follow the pattern of adding 1 more than the square of *consecutive* odd numbers.
Analyzing Series Z
Series Z is: 316, 541, 830, 1191, 1632, 2161
Let's find the differences between consecutive terms:
• 541-316 = 225
• 830-541 = 289
• 1191 - 830 = 361
• 1632- 1191 = 441
• 2161 -1632 = 529
The differences are: 225, 289, 361, 441, 529.
Let's compare these differences with squares of numbers:
• 225 = 15²
• 289 = 17²
• 361 = 19²
• 441 =  21²
• 529 =23²
The differences are n² where n takes consecutive odd values (15, 17, 19, 21, 23). The required pattern is n² + 1. Since the differences are n² instead of n² + 1, Series Z does not follow the specified pattern.
Conclusion
Based on our analysis:
• Series X follows the pattern (differences are n²+1 for consecutive odd n starting from 9).
• Series Y does not follow the pattern (differences are n² + 1, but the odd numbers are not consecutive).
Series Z does not follow the pattern (differences are n² instead of n² + 1, although the odd numbers are consecutive).
Therefore, the series that do not follow the pattern are Series Y and Series Z.