Solution

The given series is: 2, 7, 27, 107, 427, ?

Step 1: Observe the pattern. It appears each term is generated using the previous term:

\(a_{n} = a_{n-1} \times 4 - 1\)

Step 2: Verify:

• \(7 = 2 \times 4 - 1\)
• \(27 = 7 \times 4 - 1\)
• \(107 = 27 \times 4 - 1\)
• \(427 = 107 \times 4 - 1\)

Step 3: Find the next term:

\(427 \times 4 - 1 = 1708 - 1 = 1707\)

Answer: Option B → 1707