Question

Find next number in: 7, 8, 12, 21, 37, ?

• A. 66
• B. 59
• C. 62
• D. 64

Hint:

For number series, if the numbers aren't increasing or decreasing by a common multiple, check the differences between terms. If that doesn't reveal a pattern, check the differences of the differences (second-order differences).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to identify the pattern in the given number series to find the next term.
Step 2: Detailed Explanation:
The best way to find a pattern in such series is to check the differences between consecutive terms.

8 - 7 = 1
12 - 8 = 4
21 - 12 = 9
37 - 21 = 16 The series of differences is 1, 4, 9, 16.
This is a series of perfect squares:
\[ 1 = 1^2 \] \[ 4 = 2^2 \] \[ 9 = 3^2 \] \[ 16 = 4^2 \] The next difference in the sequence should be 5\(^2\) = 25.
To find the next term in the original series, we add this difference to the last term (37).
\[ \text{Next term} = 37 + 25 = 62 \] Step 3: Final Answer:
The next number in the series is 62.