Series Pattern Analysis: Identifying the Outlier

The question asks us to find the number that does not fit the pattern in the given number series: 2, 5, 10, 17, 26, 37, 50, 64. Let's examine the relationship between the position of a number in the series and the number itself.

Finding the Underlying Mathematical Rule

We can test a common pattern for number series: relating the term number (n) to the term value. Let's see if the terms follow the rule $n^2 + 1$.

• For the 1st term (n=1): $1^2 + 1 = 1 + 1 = 2$. This matches the first number in the series.
• For the 2nd term (n=2): $2^2 + 1 = 4 + 1 = 5$. This matches the second number.
• For the 3rd term (n=3): $3^2 + 1 = 9 + 1 = 10$. This matches the third number.
• For the 4th term (n=4): $4^2 + 1 = 16 + 1 = 17$. This matches the fourth number.
• For the 5th term (n=5): $5^2 + 1 = 25 + 1 = 26$. This matches the fifth number.
• For the 6th term (n=6): $6^2 + 1 = 36 + 1 = 37$. This matches the sixth number.
• For the 7th term (n=7): $7^2 + 1 = 49 + 1 = 50$. This matches the seventh number.

Checking the Final Number

Now let's check the eighth number in the series using the same pattern:

• For the 8th term (n=8): According to the pattern $n^2 + 1$, the number should be $8^2 + 1 = 64 + 1 = 65$.

The series provided has 64 as the eighth number, but the established pattern ($n^2 + 1$) predicts 65 for the eighth position. Therefore, 64 is the number that does not belong in this series.

Step-by-Step Calculation Summary

Here's a summary of the terms versus the pattern $n^2 + 1$:

The analysis clearly shows that 64 deviates from the established pattern.