Missing Sequence Terms - ISEE Lower Level Quantitative Reasoning

1. What is the missing term in the sequence $100, 50, 25, \_, 6.25$?

   $12.5$. The sequence is geometric with a common ratio of $\frac{1}{2}$, so the term after $25$ is $25 \times \frac{1}{2} = 12.5$.

2. What is the missing term in the arithmetic sequence $3, \_, 13, 18, 23$?

   $8$. The sequence is arithmetic with a common difference of $5$, so the term after $3$ is $3 + 5 = 8$.

3. What is the missing term in the sequence $2, 4, 7, 11, \_, 22$ if the differences are $+2, +3, +4, \dots$?

   $16$. The differences increase by $1$ each time starting from $+2$, so the term after $11$ is $11 + 5 = 16$.

4. What is the missing term in the sequence $-2, 1, 4, \_, 10$?

   $7$. The sequence is arithmetic with a common difference of $3$, so the term after $4$ is $4 + 3 = 7$.

5. What is the missing term in the arithmetic sequence $12, 9, 6, \_, 0$?

   $3$. The sequence is arithmetic with a common difference of $-3$, so the term after $6$ is $6 - 3 = 3$.

6. What is the missing term in the sequence $5, 6, 8, 11, \_, 20$ if the differences are $+1, +2, +3, \dots$?

   $15$. The differences increase by $1$ each time starting from $+1$, so the term after $11$ is $11 + 4 = 15$.

7. What is the missing term in the Fibonacci-type sequence $1, 1, 2, 3, \_, 8$?

   $5$. The sequence follows the Fibonacci rule where each term is the sum of the two preceding ones, so the term after $3$ is $2 + 3 = 5$.

8. What is the missing term in the sequence $1, 3, 6, 10, \_, 21$ (triangular numbers)?

   $15$. The sequence consists of triangular numbers where each term adds the next integer, so the term after $10$ is $10 + 5 = 15$.

9. What is the missing term in $1, 2, 4, 7, 11, \_$ if the differences increase by $1$ each time?

   $16$. The differences increase by $1$ each time starting from $+1$, so the term after $11$ is $11 + 5 = 16$.

10. What is the missing term in the sequence $9, 6, 8, 5, 7, \_, 6$ (alternating $-3, +2$)?

    $4$. The sequence alternates between subtracting $3$ and adding $2$, so the term after $7$ is $7 - 3 = 4$.

11. What is the missing term in the sequence $4, 9, 14, \_, 24$?

    $19$. The sequence is arithmetic with a common difference of $5$, so the term after $14$ is $14 + 5 = 19$.

12. What is the missing term in the geometric sequence $\frac{1}{2}, 1, 2, \_, 8$?

    $4$. The sequence is geometric with a common ratio of $2$, so the term after $2$ is $2 \times 2 = 4$.

13. What is the missing term in the Fibonacci-type sequence $2, 3, 5, 8, \_, 21$?

    $13$. The sequence follows the Fibonacci rule where each term is the sum of the two preceding ones, so the term after $8$ is $5 + 8 = 13$.

14. What is the missing term in the geometric sequence $5, \_, 45, 135$?

    $15$. The sequence is geometric with a common ratio of $3$, so the term after $5$ is $5 \times 3 = 15$.

15. What is the missing term in the arithmetic sequence $-4, -1, 2, \_, 8$?

    $5$. The sequence is arithmetic with a common difference of $3$, so the term after $2$ is $2 + 3 = 5$.

16. What is the missing term in the sequence of perfect cubes $1, 8, \_, 64, 125$?

    $27$. The sequence consists of perfect cubes, so the term after $8$ is $3^3 = 27$.

17. What is the missing term in the sequence $3, 6, 12, 24, \_$?

    $48$. The sequence is geometric with a common ratio of $2$, so the term after $24$ is $24 \times 2 = 48$.

18. What is the missing term in the sequence $2, 5, 10, 17, \_, 37$ if the rule is $+3, +5, +7, \dots$?

    $26$. The differences increase by $2$ each time starting from $+3$, so the term after $17$ is $17 + 9 = 26$.

19. What is the missing term in the geometric sequence $2, 6, 18, \_, 162$?

    $54$. The sequence is geometric with a common ratio of $3$, so the term after $18$ is $18 \times 3 = 54$.

20. What is the missing term in the geometric sequence $81, 27, 9, \_, 1$?

    $3$. The sequence is geometric with a common ratio of $\frac{1}{3}$, so the term after $9$ is $9 \times \frac{1}{3} = 3$.

21. What is the missing term in the sequence of perfect squares $1, 4, \_, 16, 25$?

    $9$. The sequence consists of perfect squares, so the term after $4$ is $3^2 = 9$.

22. What is the missing term in the arithmetic sequence $7, 11, 15, \_, 23$?

    $19$. The sequence is arithmetic with a common difference of $4$, so the term after $15$ is $15 + 4 = 19$.

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