Select the number from among the given options that can replace the question mark (?) in the following series. 21, 22, 44, 47, 188, ?
193
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
| Term | Operation to get next term | Next Term |
|---|---|---|
| 21 | $\small +1$ | 22 |
| 22 | $\small \times 2$ | 44 |
| 44 | $\small +3$ | 47 |
| 47 | $\small \times 4$ | 188 |
| 188 | $\small +5$ | 193 |
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.
Important Questions from Number Series
- In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 676 :: 17 : Y - Which of the following options should come in place of the question mark (?) in the given series to make it logically complete?
125, 128, 133, 140, 149,? - What should come in place of the question mark (?) in the given series?
801 800 792 765 701 ? - What should come in place of the question mark (?) in the given series?
101 110 121 134 149 ? - What should come in place of the question mark (?) in the given series?
40, 48, 58, 66, 76, ?
