Which number does not belong in the series below?
64
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 $n^2 + 1$:
| Position (n) | Series Number | Pattern ($n^2 + 1$) | Match? |
|---|---|---|---|
| 1 | 2 | $1^2 + 1 = 2$ | Yes |
| 2 | 5 | $2^2 + 1 = 5$ | Yes |
| 3 | 10 | $3^2 + 1 = 10$ | Yes |
| 4 | 17 | $4^2 + 1 = 17$ | Yes |
| 5 | 26 | $5^2 + 1 = 26$ | Yes |
| 6 | 37 | $6^2 + 1 = 37$ | Yes |
| 7 | 50 | $7^2 + 1 = 50$ | Yes |
| 8 | 64 | $8^2 + 1 = 65$ | No |
The analysis clearly shows that 64 deviates from the established pattern.
Important Questions from Numerical Reasoning
Among 150 faculty members in an institute, 55 are connected with each other through Facebook and 85 are connected through WhatsApp. 30 faculty members do not have Facebook or WhatsApp accounts. The number of faculty members connected only through Facebook accounts is ______________.
X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km?
- Two numbers are, respectively, 28% and 25% less than a third number. What percent is the first number of the second number?
A dealer sold three-forth (3/4th) of his articles at a gain of 20% and the remaining articles at the cost price. Find the gain earned by him in the whole transaction.
78, 65, 82, 69, 86, ?
