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:

To solve sequence problems, analyze the differences or ratios between consecutive terms. Look for arithmetic or geometric progressions or other patterns.

Answer 1

The Correct Option is B

Step 1: Analyze the differences between consecutive terms.

The given sequence is \( 6, 9, 14, x, 30, 41 \). Calculate the differences between consecutive terms:

\[ 9 - 6 = 3, \quad 14 - 9 = 5. \]

Let \( x \) be the next term:

\[ x - 14 = 7 \quad \Rightarrow \quad x = 21. \]

For the subsequent terms:

\[ 30 - 21 = 9, \quad 41 - 30 = 11. \] Step 2: Confirm the pattern.

The differences between consecutive terms form the sequence:

\[ 3, 5, 7, 9, 11. \]

This is an arithmetic progression with a common difference of \( 2 \), verifying the correctness of the solution.

Thus, the value of \( x \) is \( \boxed{21} \).