Numerical Series Examples

1. Examine the difference between adjacent numbers.

→ In a simple series, the difference between two consecutive numbers is constant.

Example: 27, 24, 21, 18, __

Rule: There is a difference of (-3) between each item. The missing number in this case is 15.

→ In a more complex series, the differences between numbers may be dynamic rather than fixed, but there is still a clear logical rule.

Example: 3, 4, 6, 9, 13, 18, __

Rule: Add 1 to the difference between two adjacent items. After the first number add 1, after the second number add 2, and after the third number add 3, etc. In this case, the missing number is 24.

2. See whether there is a multiplication or division pattern between two adjacent numbers.

Example: 64, 32, 16, 8, __

Rule: Divide each number by 2 to get the next number in the series. The missing number is 4.

3. Check whether adjacent numbers in the series change based on a logical pattern.

Example: 2, 4, 12, 48, __

Rule: Multiply the first number by 2, the second number by 3 and the third number by 4, etc. The missing item is 240.

4. See if you can find a rule that involves using two or more basic arithmetic functions (+, -, ÷, x). In the series below, the functions alternate in an orderly fashion.

Example: 5, 7, 14, 16, 32, 34, __

Rule: Add 2, multiply by 2, add 2, multiply by 2, etc. The missing item is 68. Tip: Series in this category are easy to identify. Just look for numbers that do not appear to have a set pattern.

Important: In a series that involves two or more basic arithmetic functions, the differences between adjacent items effectively create their own series. We recommend that you try to identify each pattern separately.

Example: 4, 6, 2, 8, 3, __

Rule: In this series, the differences themselves create a series: +2, ÷3, x4, -5. The numbers advance by intervals of 1, and the arithmetic functions change in an orderly sequence. The next arithmetic function in the series should be +6, and so the next item in the series is 9 (3+6 = 9).