Question

In the sequence \( 6, 9, 14, x, 30, 41 \), a possible value of \( x \) is:

• A. 25
• B. 21
• C. 18
• D. 20

Hint:

When solving sequence problems, analyze the differences or ratios between consecutive terms to identify patterns.

Answer 1

The Correct Option is B

Step 1: Identify the pattern in the sequence.
The given sequence is \( 6, 9, 14, x, 30, 41 \). To find the missing value \( x \), observe the differences between consecutive terms: \[ 9 - 6 = 3, \quad 14 - 9 = 5. \] The differences are increasing by 2: \( 3, 5, \ldots \). The next difference should be \( 7 \): \[ x - 14 = 7 \implies x = 14 + 7 = 21. \] Verify the pattern for the next terms: \[ 30 - 21 = 9, \quad 41 - 30 = 11. \] The differences \( 7, 9, 11 \) confirm the pattern. Final Answer: \[ \boxed{21} \]