Number Patterns and Sequences Flashcards

What is the next number in the following geometric sequence: 80, 40, 20, 10, ___?

Answer: 5

This is a geometric sequence where each term is found by dividing the previous term by 2 (or multiplying by 1/2). 80 / 2 = 40, 40 / 2 = 20, and 20 / 2 = 10. Therefore, the next term in the sequence is 10 / 2 = 5.

A concert hall has 20 seats in the first row. Each subsequent row has 3 more seats than the row in front of it. How many seats are in the 8th row?

Answer: 41

This is an arithmetic sequence that starts at 20 with a common difference of 3. You can list the terms: Row 1=20, R2=23, R3=26, R4=29, R5=32, R6=35, R7=38, R8=41. Alternatively, the formula for the nth term is a + (n-1)d, where a=20, n=8, and d=3. This gives 20 + (8-1)*3 = 20 + 7*3 = 20 + 21 = 41.

Consider a visual pattern made of square tiles. Figure 1 has 1 tile, Figure 2 has 4 tiles, and Figure 3 has 9 tiles, arranged in squares. If this pattern continues, how many tiles will be in Figure 6?

Answer: 36

The pattern shows that the number of tiles is the figure number multiplied by itself (the figure number squared). Figure 1: 1×1=1. Figure 2: 2×2=4. Figure 3: 3×3=9. Following this rule, Figure 6 will have 6×6 = 36 tiles.

Which of the following is the next number in the sequence: 2, 3, 5, 8, 12, ___?

Answer: 17

The pattern in this sequence is not simple addition; instead, the amount added increases by one each time. To get from 2 to 3, you add 1. From 3 to 5, you add 2. From 5 to 8, you add 3. From 8 to 12, you add 4. Therefore, to find the next number, you must add 5 to 12, which results in 17.

The table below shows a relationship between an input number, 'n', and an output number. Which rule describes this relationship? | Input (n) | Output | |---|---| | 2 | 7 | | 3 | 10 | | 4 | 13 | | 5 | 16 |

Answer: 3n + 1

To find the correct rule, test each option with the input values. For the rule 3n + 1: when n=2, the output is 3(2)+1=7. When n=3, the output is 3(3)+1=10. When n=4, the output is 3(4)+1=13. Since this rule works for all the pairs in the table, it is the correct one. The other options fail for at least one of the pairs.

Find the missing number in the following arithmetic sequence: 4, 10, ___, 22, 28.

Answer: 16

In an arithmetic sequence, the same number is added to get from one term to the next. This is called the common difference. By subtracting consecutive terms (28 - 22 = 6 and 10 - 4 = 6), we find the common difference is 6. To find the missing term, add 6 to the term before it: 10 + 6 = 16. You can verify this by adding 6 again: 16 + 6 = 22.