Missing Sequence Terms - ISEE Middle Level Quantitative Reasoning

1. What is the missing term in the sequence $2, 5, 11, 23, \_, 95$?

   $47$. Each term follows the rule of multiplying the previous by $2$ and adding $1$, so apply to $23$.

2. What is the missing term in the sequence $1, 3, 6, 10, \_, 21$?

   $15$. The triangular number sequence follows $\frac{n(n+1)}{2}$ for $n=1$ to $5$, so the missing term is for $n=5$.

3. What is the missing term in the square-number sequence $1, 4, 9, \_, 25$?

   $16$. The sequence consists of squares of consecutive integers from $1^2$ to $5^2$, so the missing term is $4^2$.

4. What is the missing term in the triangular-number sequence $1, 3, 6, \_, 15$?

   $10$. The triangular number sequence is the sum of the first $n$ integers, so the missing term is for $n=4$.

5. What is the missing term in the arithmetic sequence $\frac{1}{2}, 1, \frac{3}{2}, \_, \frac{5}{2}$?

   $2$. The arithmetic sequence has a common difference of $\frac{1}{2}$, so the missing term is found by adding $\frac{1}{2}$ to $\frac{3}{2}$.

6. What is the missing term in the sequence $3^0, 3^1, \_, 3^3, 3^4$?

   $3^2$. The sequence is powers of $3$ with consecutive exponents from $0$ to $4$, so the missing term has exponent $2$.

7. What is the missing term in the arithmetic sequence $-3, 1, 5, \_, 13$?

   $9$. The arithmetic sequence has a common difference of $4$, so the missing term is found by adding $4$ to $5$.

8. What is the missing term in the arithmetic sequence $20, 15, 10, \_, 0$?

   $5$. The arithmetic sequence has a common difference of $-5$, so the missing term is found by subtracting $5$ from $10$.

9. What is the missing term in the sequence $1, 2, 4, 7, \_, 16$?

   $11$. The differences increase by $1$ each time ($+1, +2, +3, +4$), so add $4$ to $7$.

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

    $12.5$. The geometric sequence has a common ratio of $\frac{1}{2}$, so the missing term is found by multiplying $25$ by $\frac{1}{2}$.

11. What is the missing term in the cube-number sequence $1, 8, 27, \_, 125$?

    $64$. The sequence consists of cubes of consecutive integers from $1^3$ to $5^3$, so the missing term is $4^3$.

12. What is the missing term in the arithmetic sequence $4, 7, 10, \_, 16$?

    $13$. The arithmetic sequence has a common difference of $3$, so the missing term is found by adding $3$ to $10$.

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

    $2$. The geometric sequence has a common ratio of $2$, so the missing term is found by multiplying $1$ by $2$.

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

    $13$. In this Fibonacci-type sequence, each term is the sum of the two preceding ones, so add $5$ and $8$.

15. What is the missing term in the sequence $\frac{1}{3}, \frac{1}{6}, \frac{1}{12}, \_, \frac{1}{48}$?

    $\frac{1}{24}$. The geometric sequence has a common ratio of $\frac{1}{2}$, so the missing term is found by multiplying $\frac{1}{12}$ by $\frac{1}{2}$.

16. What is the missing term in the sequence of powers $2^1, 2^2, 2^3, \_, 2^5$?

    $2^4$. The sequence is powers of $2$ with consecutive exponents from $1$ to $5$, so the missing term has exponent $4$.

17. What is the missing term in the sequence $0.2, 0.4, 0.8, \_, 3.2$?

    $1.6$. The geometric sequence has a common ratio of $2$, so the missing term is found by multiplying $0.8$ by $2$.

18. What is the missing term in the alternating sequence $2, 5, 4, 7, 6, \_$?

    $9$. The sequence consists of two interleaved arithmetic sequences increasing by $2$, with odd positions starting at $2$ and even at $5$, so the sixth term follows the even sequence.

19. What is the missing term in the geometric sequence $3, 6, 12, \_, 48$?

    $24$. The geometric sequence has a common ratio of $2$, so the missing term is found by multiplying $12$ by $2$.

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

    $16$. The sequence alternates between multiplying by $4$ and dividing by $2$, so multiply $4$ by $4$.

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

    $3$. The geometric sequence has a common ratio of $\frac{1}{3}$, so the missing term is found by multiplying $9$ by $\frac{1}{3}$.

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