IAAT - Iowa Algebra Aptitude Number Patterns and Sequences Questions and Answers

Question 1

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

Accepted Answer

5

Answer

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.

Question 2

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?

Accepted Answer

41

Answer

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.

Question 3

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?

Accepted Answer

36

Answer

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.

Question 4

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

Accepted Answer

17

Answer

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.

Question 5

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 |

Accepted Answer

3n + 1

Answer

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.

IAAT - Iowa Algebra Aptitude Test Practice Test

IAAT - Iowa Algebra Aptitude Test Practice Test

IAAT - Iowa Algebra Aptitude Number Patterns and Sequences Questions and Answers