Question

What is the value of \(X\) in the sequence \(20, 10, 10, 15, 30, 75, X\)?

• A. 225
• B. 125
• C. 150
• D. 100

Hint:

Look for increasing fractional multipliers in number series. Many patterns follow arithmetic progression in multipliers.

Answer 1

The Correct Option is A

Concept: This is a number pattern question. We observe multiplication and division alternately. Sequence: \[ 20, 10, 10, 15, 30, 75, X \] Step 1: Find the pattern between consecutive terms.
From \(20\) to \(10\): \[ 20 \div 2 = 10 \] From \(10\) to \(10\): \[ 10 \times 1 = 10 \] From \(10\) to \(15\): \[ 10 \times \frac{3}{2} = 15 \]

Step 2: Continue the multiplication pattern.
From \(15\) to \(30\): \[ 15 \times 2 = 30 \] From \(30\) to \(75\): \[ 30 \times \frac{5}{2} = 75 \] Pattern: \[ \times \frac{1}{2}, \times 1, \times \frac{3}{2}, \times 2, \times \frac{5}{2} \]

Step 3: Find the next multiplier.
Next multiplier: \[ \times 3 \] So: \[ 75 \times 3 = 225 \]

Step 4: Final conclusion.
Hence, \[ X = \boxed{225} \]