Missing Terms in Sequences - ISEE Middle Level Mathematics Achievement

1. What is the missing term in the geometric sequence $81, 27, \_, 3$?

   $9$. The geometric sequence has a common ratio of $\frac{1}{3}$, so multiply $27$ by $\frac{1}{3}$ to find the missing term.

2. What is the missing term in the sequence $3, 6, 12, 24, \_, 96$ (each term doubles)?

   $48$. Each term doubles the previous, so multiply $24$ by $2$ to find the missing term.

3. What is the missing term in the alternating sequence $10, 7, 14, 11, \_, 15$?

   $18$. The alternating sequence interweaves two arithmetic progressions with common difference $4$, placing $18$ in the fifth position.

4. What is the missing term in the arithmetic sequence $0.3, 0.6, \_, 1.2$?

   $0.9$. The arithmetic sequence has a common difference of $0.3$, so add $0.3$ to $0.6$ to find the missing term.

5. What is the missing term in the geometric sequence $2, 6, \_, 54$?

   $18$. The geometric sequence has a common ratio of $3$, so multiply $6$ by $3$ to find the missing term.

6. What is the missing term in the sequence $1, 11, 21, \_, 41$ (numbers ending in $1$ with step $10$)?

   $31$. The arithmetic sequence has a common difference of $10$, so add $10$ to $21$ to find the missing term.

7. What is the missing term in the sequence $1, 8, 27, \_, 125$ (perfect cubes)?

   $64$. The sequence consists of consecutive perfect cubes, so the fourth term is $4^3$.

8. What is the missing term in the alternating sequence $1, -2, 3, -4, \_, -6$?

   $5$. The sequence alternates positive and negative signs with consecutive integers, so the fifth term is positive $5$.

9. What is the missing term in the sequence $1, 2, 4, 7, \_, 16$ (add $1,2,3,\dots$)?

   $11$. The sequence adds consecutive integers starting from $1$, so add $4$ to $7$ to find the missing term.

10. What is the missing term in the arithmetic sequence $20, 16, 12, \_, 4$?

    $8$. The arithmetic sequence has a common difference of $-4$, so subtract $4$ from $12$ to find the missing term.

11. What is the missing term in the sequence $2, 3, 5, 8, \_, 21$ (each term is sum of previous two)?

    $13$. Each term is the sum of the two preceding terms, so add $5$ and $8$ to find the missing term.

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

    $15$. The geometric sequence has a common ratio of $3$, so multiply $5$ by $3$ to find the missing term.

13. What is the missing term in the sequence $1, 4, 9, \_, 25$ (perfect squares)?

    $16$. The sequence consists of consecutive perfect squares, so the fourth term is $4^2$.

14. What is the missing term in the sequence $2, 5, 10, 17, \_, 37$ (add consecutive odd numbers)?

    $26$. The sequence adds consecutive odd numbers starting from $3$, so add $9$ to $17$ to find the missing term.

15. What is the missing term in the arithmetic sequence $-4, -1, \_, 5, 8$?

    $2$. The arithmetic sequence has a common difference of $3$, so add $3$ to $-1$ to find the missing term.

16. What is the missing term in the sequence $4, 9, 16, \_, 36$ (squares starting at $2^2$)?

    $25$. The sequence consists of squares of consecutive integers starting from $2$, so the fourth term is $5^2$.

17. What is the missing term in the arithmetic sequence $\frac{1}{2}, 1, \_, 2$?

    $\frac{3}{2}$. The arithmetic sequence has a common difference of $\frac{1}{2}$, so add $\frac{1}{2}$ to $1$ to find the missing term.

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

    $15$. The sequence consists of triangular numbers, so add $5$ to $10$ to find the missing term.

19. What is the missing term in the arithmetic sequence $3, 7, \_, 15, 19$?

    $11$. The arithmetic sequence has a common difference of $4$, so add $4$ to $7$ to find the missing term.

20. What is the missing term in the sequence $2, 6, 12, 20, \_, 42$ (pronic numbers $n(n+1)$)?

    $30$. The sequence consists of pronic numbers $n(n+1)$, so for $n=5$ the term is $5 \times 6$.

21. What is the missing term in the geometric sequence $\frac{1}{4}, \_, 1, 2$?

    $\frac{1}{2}$. The geometric sequence has a common ratio of $2$, so multiply $\frac{1}{4}$ by $2$ to find the missing term.

22. What is the missing term in the sequence $100, 50, 25, \_, 6.25$ (each term halves)?

    $12.5$. Each term is half the previous, so divide $25$ by $2$ to find the missing term.

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