Odd One Out: Explanation

The given sequence is 2, 5, 10, 17, 26, 37, 50, 64. We need to identify the number that does not follow the pattern established by the rest of the sequence.

Pattern Analysis

To find the pattern in the given sequence, we can observe the differences between consecutive terms:

- The difference between the first and second term is 5 - 2 = 3.
- The difference between the second and third term is 10 - 5 = 5.
- The difference between the third and fourth term is 17 - 10 = 7.
- The difference between the fourth and fifth term is 26 - 17 = 9.
- The difference between the fifth and sixth term is 37 - 26 = 11.
- The difference between the sixth and seventh term is 50 - 37 = 13.
- The difference between the seventh and eighth term is 64 - 50 = 14.

We can notice that the differences between consecutive terms are increasing by 2 each time. This suggests that the pattern in the given sequence is a quadratic sequence where the nth term can be represented as n^2 + 1.

Applying the Pattern

Now, let's apply the pattern to each term in the given sequence:

- The first term is 1^2 + 1 = 2.
- The second term is 2^2 + 1 = 5.
- The third term is 3^2 + 1 = 10.
- The fourth term is 4^2 + 1 = 17.
- The fifth term is 5^2 + 1 = 26.
- The sixth term is 6^2 + 1 = 37.
- The seventh term is 7^2 + 1 = 50.
- The eighth term is 8^2 + 1 = 65.

Identifying the Odd One Out

From the above analysis, we can see that the eighth term in the given sequence, 64, does not follow the pattern established by the rest of the sequence. Therefore, the odd one out is option D) 64.

64