Question

Find the missing number?

• A. 16
• B. 13
• C. 18
• D. 15

Hint:

To solve sequence problems, look at the differences between terms. Often, the differences themselves form a recognizable pattern, such as squares or cubes.

Answer 1

The Correct Option is D

Let's analyze the given sequence: \[ 1, 2, 6, ?, 31, 56, 92. \] Look at the pattern in the differences between consecutive terms:
- \( 2 - 1 = 1 \)
- \( 6 - 2 = 4 \)
- \( ? - 6 = ? \)
- \( 31 - ? = ? \)
- \( 56 - 31 = 25 \)
- \( 92 - 56 = 36 \)
We can observe that the differences are increasing by a consistent pattern: \[ 1, 4, ?, 25, 36. \] The differences between the numbers are increasing by successive squares: \[ 1 = 1^2, \quad 4 = 2^2, \quad 25 = 5^2, \quad 36 = 6^2. \] Thus, the missing difference should be \( 3^2 = 9 \). Therefore, \[ ? - 6 = 9 \quad \Rightarrow \quad ? = 6 + 9 = 15. \] Thus, the missing number is 15.