IAAT - Iowa Algebra Aptitude Number Patterns and Sequences Questions and Answers — Questions and Answers
Question 1: What is the next number in the following geometric sequence: 80, 40, 20, 10, ___?
- 2
- 0
- 5 (Correct answer)
- 8
Correct 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.
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?
- 44
- 41 (Correct answer)
- 38
- 24
Correct 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.
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?
- 12
- 25
- 18
- 36 (Correct answer)
Correct 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.
Question 4: Which of the following is the next number in the sequence: 2, 3, 5, 8, 12, ___?
- 17 (Correct answer)
- 16
- 15
- 18
Correct 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.
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 |
- n + 5
- 2n + 3
- 3n + 1 (Correct answer)
- 4n - 1
Correct 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.
Question 6: Find the missing number in the following arithmetic sequence: 4, 10, ___, 22, 28.
- 15
- 16 (Correct answer)
- 17
- 18
Correct 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.
IAAT - Iowa Algebra Aptitude Number Patterns and Sequences Questions and Answers
What is the next number in the following geometric sequence: 80, 40, 20, 10, ___?