Number Sequence Patterns Flashcards

Which number logically follows in this sequence? 3, 4, 8, 17, 33, ...

Answer: 58

The pattern is to add the square of consecutive integers, starting with 1. First, 3 + 1^2 = 3 + 1 = 4. Then, 4 + 2^2 = 4 + 4 = 8. Next, 8 + 3^2 = 8 + 9 = 17. Following that, 17 + 4^2 = 17 + 16 = 33. The final step is 33 + 5^2 = 33 + 25 = 58.

Identify the next number in the following series: 81, 27, 9, 3, 1, ...

Answer: 1/3

This is a geometric progression where each subsequent number is the result of dividing the previous number by 3. 81 / 3 = 27. 27 / 3 = 9. 9 / 3 = 3. 3 / 3 = 1. Therefore, the next number is 1 / 3.

A data processing script generates a numerical sequence based on a two-step alternating rule. Given the sequence 5, 10, 8, 16, 14, 28, ..., what is the next number?

Answer: 26

The sequence follows an alternating pattern of two operations: multiply by 2, then subtract 2. 5 * 2 = 10. 10 - 2 = 8. 8 * 2 = 16. 16 - 2 = 14. 14 * 2 = 28. The next operation is to subtract 2, so 28 - 2 = 26.

Which of the following numbers completes the sequence: 4, 5, 9, 14, 23, ...?

Answer: 37

This sequence follows the Fibonacci rule, where each number is the sum of the two preceding numbers. 4 + 5 = 9. 5 + 9 = 14. 9 + 14 = 23. Therefore, the next number is 14 + 23 = 37.

Find the missing number in the sequence: 7, 10, 9, 12, 11, 14, ___, 16.

Answer: 13

This is an interleaved sequence. There are two independent patterns. The first pattern starts at 7 and subtracts 1 then adds 2, but the simpler pattern is to see two alternating series. One is 7, 9, 11, ... (add 2). The other is 10, 12, 14, 16 (add 2). The missing number belongs to the first pattern, so 11 + 2 = 13.

What is the next number in this series? 2, 3, 5, 9, 17, ...

Answer: 33

The difference between consecutive numbers doubles each time. 3 - 2 = 1. 5 - 3 = 2. 9 - 5 = 4. 17 - 9 = 8. The next difference will be 16. Therefore, the next number is 17 + 16 = 33.