Question

What will come in place of question mark (?) in the following series:
12, 6, 6, 9, 18, ?

• A. 42
• B. 45
• C. 50
• D. 55

Hint:

When a series seems complex, check the relationship between terms (addition, subtraction, multiplication, division). If the relationship isn't constant, check if the relationship itself follows a simple pattern.

Answer 1

The Correct Option is B

Step 1: Identify the pattern connecting the terms in the series. The series is not arithmetic or a simple geometric progression. Let's find the multiplier between each consecutive pair of numbers.

From 12 to 6: \( 12 \times 0.5 = 6 \)
From 6 to 6: \( 6 \times 1 = 6 \)
From 6 to 9: \( 6 \times 1.5 = 9 \)
From 9 to 18: \( 9 \times 2 = 18 \)

Step 2: Analyze the sequence of multipliers. The multipliers are 0.5, 1, 1.5, 2. This forms a simple arithmetic progression where 0.5 is added at each step.
Step 3: Determine the next multiplier and calculate the next term. The next multiplier in the sequence will be \( 2 + 0.5 = 2.5 \). The next term in the series is found by multiplying the last term (18) by this multiplier. Next Term = \( 18 \times 2.5 = 45 \).