Number series is a very easy and important topic of logical reasoning. Here, we will see questions related to series of numbers which follow a particular pattern. Once you identify the pattern, finding the missing number becomes extremely straightforward.
Common Number Series Patterns
To solve number series questions quickly in the CSAT paper, you must familiarize yourself with these standard patterns:
- Difference Series (Addition/Subtraction): The difference between consecutive numbers is constant or follows a sequence (e.g., 2, 4, 6, 8…).
- Product Series (Multiplication/Division): Each term is multiplied or divided by a constant to get the next term (e.g., 3, 9, 27, 81…).
- Alternate Series: Two or more series are interleaved. You need to analyze alternating terms separately (e.g., 1, 10, 3, 20, 5, 30…).
- Prime Number Series: Terms are consecutive prime numbers (e.g., 2, 3, 5, 7, 11, 13…).
- Squares and Cubes Series: Terms are squares or cubes of natural numbers, or have a constant difference from them (e.g., n² + 1 or n³ – 1).
Step-by-Step Solving Strategy
- Check the rate of change: If the numbers increase gradually, the pattern is likely addition or subtraction. If they increase rapidly, it is likely multiplication or exponent-based.
- Find differences: If the pattern isn’t obvious, write down the difference between consecutive terms. Often, a secondary pattern (difference-of-difference) will emerge.
- Check for alternate terms: If the series fluctuates (increases, decreases, increases), look for alternate series.
Sample Solved Questions
Example 1: Find the missing number: 4, 9, 19, 39, 79, ?
Solution: Let’s look at the relationship between consecutive terms: * 4 * 2 + 1 = 9 * 9 * 2 + 1 = 19 * 19 * 2 + 1 = 39 * 39 * 2 + 1 = 79 Following the same pattern: 79 * 2 + 1 = 159. Therefore, the missing number is 159.
Example 2: Find the missing term: 2, 5, 10, 17, 26, ?
Solution: Let’s analyze the terms as squares: * 1² + 1 = 2 * 2² + 1 = 5 * 3² + 1 = 10 * 4² + 1 = 17 * 5² + 1 = 26 Following the pattern, the next term is 6² + 1 = 37.