Question

Find the missing term in the series: \[ 6,\;13,\;27,\;55,\;\_\_\_,\;223,\;447,\;895 \]

• A. \(110\)
• B. \(111\)
• C. \(112\)
• D. \(113\)

Hint:

In geometric-like number series, always check multiplication followed by addition or subtraction.

Answer 1

The Correct Option is B

Concept: Observe the pattern: Each term is obtained by: \[ (\text{previous term} \times 2)+1 \]

Step 1: Verify the pattern.
\[ 6 \times 2+1=13 \] \[ 13 \times 2+1=27 \] \[ 27 \times 2+1=55 \]

Step 2: Find the missing term.
\[ 55 \times 2+1=111 \]

Step 3: Check the remaining terms.
\[ 111 \times 2+1=223 \] \[ 223 \times 2+1=447 \] \[ 447 \times 2+1=895 \] Pattern matches perfectly. Thus, the missing term is: \[ \boxed{111} \]