Question

A number series is given below with one term missing.
Choose the correct alternative that will continue the same pattern and replace the question mark in the given series: \[ 240,\ \ ?,\ \ 120,\ 40,\ 10,\ 2 \]

• A. \(180\)
• B. \(240\)
• C. \(420\)
• D. \(480\)

Hint:

Always check ratios between consecutive terms in a number series. Many series follow a pattern of division or multiplication with increasing numbers.

Answer 1

The Correct Option is B

Concept: In number series, patterns often involve multiplication or division by increasing or decreasing values. A common approach is to check the ratio between consecutive terms to identify a consistent pattern.

Step 1: Observe the given series carefully. \[ 240,\ \ ?,\ \ 120,\ 40,\ 10,\ 2 \] We start checking from the known part: \[ 120 \to 40 \to 10 \to 2 \]

Step 2: Find the pattern in known terms. \[ 120 \div 3 = 40 \] \[ 40 \div 4 = 10 \] \[ 10 \div 5 = 2 \] So, the pattern is: \[ \div 3,\ \div 4,\ \div 5 \]

Step 3: Extend the pattern backwards. Before dividing by 3, the number must have been: \[ 120 \times 2 = 240 \] So the pattern becomes: \[ \div 2,\ \div 3,\ \div 4,\ \div 5 \]

Step 4: Find the missing term. \[ 240 \div 2 = 120 \] Thus, the missing term is: \[ 240 \]

Step 5: Verify the full sequence. \[ 240 \div 2 = 120,\quad 120 \div 3 = 40,\quad 40 \div 4 = 10,\quad 10 \div 5 = 2 \] Pattern is consistent. \[ \boxed{240} \]