Series: 2, 7, 27, 107, 427, ?

Step 1: Look at the pattern.
Each term seems to follow: $$a_{n+1} = 4 \times a_n - 1$$

Step 2: Verify the rule.
• 2 → 4×2 - 1 = 7 ✅
• 7 → 4×7 - 1 = 27 ✅
• 27 → 4×27 - 1 = 107 ✅
• 107 → 4×107 - 1 = 427 ✅

Step 3: Find the next term.
• 427 → 4×427 - 1 = 1707 ✅

Missing Term: 1707

Answer: Option 2

Grid (row-wise):
(72, 24, 6)    (96, 16, 12)    (108, ?, 18)

Pattern: In each row, $$\text{third} = 2 \times \frac{\text{first}}{\text{second}}$$

Check Row 1: \( 2 \times \frac{72}{24} = 2 \times 3 = 6 \) ✅
Check Row 2: \( 2 \times \frac{96}{16} = 2 \times 6 = 12 \) ✅

Apply to Row 3: Let the missing number be \(x\). $$18 = 2 \times \frac{108}{x}  $$

$$\;\Rightarrow\;18= \frac{216}{x}  $$

$$\;\Rightarrow\; x = \frac{216}{18} = 12$$

Missing Number: 12

Answer: Option 1

Given Series: 7, 14, 28, ...

Pattern: Each term is multiplied by 2.

Formula for the nth term: Tn = 7 × 2n-1

Calculation:

T₁₀ = 7 × 2^10-1 = 7 × 2⁹ = 7 × 512 = 3584

Answer:

The 10th term is 3584.