Predicting Later Terms - SSAT Middle Level Quantitative

1. What is the next term in the pattern $4, 9, 19, 39, 79, \dots$?

   $159$. Each term is obtained by doubling the previous and adding $1$.

2. What is the next term in the pattern $\frac{1}{2}, 1, \frac{3}{2}, 2, \frac{5}{2}, \dots$?

   $3$. The arithmetic sequence increases by $\frac{1}{2}$ each time, so add $\frac{1}{2}$ to the last term.

3. What is the next term in the geometric pattern $2, 6, 18, 54, \dots$?

   $162$. The geometric sequence has a common ratio of $3$, so multiply the last term by $3$ to find the next.

4. What is the next term in the pattern $3, 6, 10, 15, 21, \dots$?

   $28$. The sequence is triangular numbers where differences increase by $1$ starting from $3$, so add $7$ to the last term.

5. What is the $7$th term of the geometric sequence $5, 10, 20, 40, \dots$?

   $320$. The geometric sequence has first term $5$ and common ratio $2$, so the $n$th term is $5 \times 2^{n-1}$.

6. What is the next term in the pattern $2, 3, 5, 8, 12, \dots$?

   $17$. Differences increase by $1$ starting from $+1$, so add $5$ to the last term.

7. What is the $8$th term of the pattern $1, 3, 6, 10, 15, \dots$?

   $36$. The sequence is triangular numbers, where the $n$th term is $\frac{n(n+1)}{2}$.

8. What is the next term in the alternating pattern $10, 7, 14, 11, 18, 15, \dots$?

   $22$. The pattern alternates subtracting $3$ and adding $7$, so add $7$ after the last subtraction.

9. What is the next term in the pattern $\frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \dots$?

   $\frac{6}{7}$. Both numerator and denominator increase by $1$ each time, starting from $\frac{2}{3}$.

10. What is the $12$th term of the square-number pattern $1, 4, 9, 16, \dots$?

    $144$. The sequence is squares of consecutive integers starting from $1$, so the $n$th term is $n^2$.

11. What is the next term in the pattern $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \dots$?

    $\frac{1}{32}$. The geometric sequence has a common ratio of $\frac{1}{2}$, so multiply the last term by $\frac{1}{2}$.

12. What is the $6$th term of the cube-number pattern $1, 8, 27, 64, \dots$?

    $216$. The sequence is cubes of consecutive integers starting from $1$, so the $n$th term is $n^3$.

13. What is the next term in the pattern $100, 50, 25, 12.5, \dots$?

    $6.25$. The geometric sequence has a common ratio of $\frac{1}{2}$, so multiply the last term by $\frac{1}{2}$.

14. What is the next term in the pattern $1, 8, 27, 64, \dots$?

    $125$. The sequence consists of cubes of consecutive integers, so cube the next integer after $4$.

15. What is the next term in the pattern $2, 6, 12, 20, 30, \dots$?

    $42$. The sequence follows $n(n+1)$ for consecutive integers $n$ starting from $1$, so use $n=6$.

16. What is the next term in the Fibonacci-type pattern $1, 1, 2, 3, 5, 8, \dots$?

    $13$. The sequence follows the Fibonacci rule where each term is the sum of the two preceding ones.

17. What is the $10$th term of the arithmetic sequence $3, 8, 13, 18, \dots$?

    $48$. The arithmetic sequence has first term $3$ and common difference $5$, so the $n$th term is $3 + (n-1) \times 5$.

18. What is the next term in the pattern $1, 4, 9, 16, 25, \dots$?

    $36$. The sequence consists of squares of consecutive integers, so square the next integer after $5$.

19. What is the next term in the arithmetic pattern $7, 11, 15, 19, \dots$?

    $23$. The sequence is arithmetic with a common difference of $4$, so add $4$ to the last term to find the next.

Study these flashcards