Analyzing the Number Series Pattern

The question asks us to find the missing number in the given series: 21, 22, 44, 47, 188, ?

Let's examine the relationship between consecutive terms in the series to identify the pattern.

• From 21 to 22: We add 1 ($\small 21 + 1 = 22$).
• From 22 to 44: We multiply by 2 ($\small 22 \times 2 = 44$).
• From 44 to 47: We add 3 ($\small 44 + 3 = 47$).
• From 47 to 188: We multiply by 4 ($\small 47 \times 4 = 188$).

The pattern observed is an alternating sequence of addition and multiplication. The number being added or multiplied increases by 1 in each step:

• Step 1: Add 1
• Step 2: Multiply by 2
• Step 3: Add 3
• Step 4: Multiply by 4

Following this pattern, the next step (Step 5) should be to add 5 to the last number in the series (188).

Calculation for the next term:

$\small 188 + 5 = 193$

Therefore, the missing number in the series is 193.

Let's summarize the pattern:

• $\small 21 \xrightarrow{+1} 22$
• $\small 22 \xrightarrow{\times 2} 44$
• $\small 44 \xrightarrow{+3} 47$
• $\small 47 \xrightarrow{\times 4} 188$
• $\small 188 \xrightarrow{+5} 193$

The series continues as 21, 22, 44, 47, 188, 193.

The number 193 matches one of the given options.

Revision Table: Number Series Pattern

Additional Information: Solving Number Series Questions

Number series questions are common in reasoning tests and competitive exams. To solve them, look for patterns involving:

• Arithmetic Operations: Addition, subtraction, multiplication, division between consecutive terms.
• Differences: Calculate the difference between consecutive terms. The differences themselves might form a pattern (e.g., increasing or decreasing by a constant, squares, cubes, etc.).
• Ratios: Check for a common ratio between terms (geometric progression).
• Alternating Patterns: The pattern might alternate between two different operations or sequences.
• Squares, Cubes, or other powers: Terms might be related to squares or cubes of numbers, sometimes with an addition or subtraction.
• Fibonacci-like series: A term might be the sum of the previous two terms.

Always test the identified pattern across all given terms in the series to ensure it holds true before predicting the next term.