Data-Based Predictions - ISEE Lower Level Quantitative Reasoning

1. What is the predicted total after $5$ days if a plant grows $3$ cm per day starting at $2$ cm?

   $17$ cm. The plant grows linearly at 3 cm per day, so add $3 \times 5$ to the initial 2 cm.

2. What is the next term in the sequence $1, 1, 2, 3, 5, 8, \dots$?

   $13$. This is the Fibonacci sequence, where each term is the sum of the two preceding ones.

3. What is the predicted value of $y$ when $x=4$ if the pattern is $(1,2),(2,4),(3,8)$?

   $16$. The pattern shows $y = 2^x$, so substitute $x=4$ into the equation.

4. What is the next term in the sequence $5, 9, 17, 33, \dots$?

   $65$. Each term is obtained by multiplying the previous by 2 and subtracting 1.

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

   $6.25$. Each term is half of the previous in this geometric sequence with ratio $\frac{1}{2}$.

6. What is the next term in the sequence $10, 9, 7, 4, 0, \dots$?

   $-5$. The differences decrease by 1 each time, becoming more negative, so subtract 5 from the last term.

7. What is the next term in the sequence $4, 12, 36, 108, \dots$?

   $324$. This geometric sequence has a common ratio of 3, so multiply the last term by 3.

8. What is the predicted value of $y$ when $x=5$ if the pattern is $(1,3),(2,5),(3,7),(4,9)$?

   $11$. The linear pattern follows $y = 2x + 1$, so substitute $x=5$ into the equation.

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

   $25$. The sequence consists of perfect squares, so the next term is $5^2$.

10. What is the next term in the sequence $3, 8, 15, 24, \dots$?

    $35$. The differences increase by 2 each time, so add 11 to the last term.

11. What is the common ratio in the geometric sequence $3, 6, 12, 24, \dots$?

    $2$. The common ratio is determined by dividing consecutive terms in the geometric sequence, resulting in 2 each time.

12. What is the next term in the sequence $2, 5, 10, 17, \dots$?

    $26$. The differences between terms increase by 2 each time, so add 9 to the last term.

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

    $17$. The differences increase by 1 each time, so add 5 to the last term.

14. What is the predicted value of $y$ when $x=6$ if $y=2x$ and the pattern continues?

    $12$. The linear pattern is $y = 2x$, so substitute $x=6$ into the equation.

15. What is the next term in the sequence $1, 3, 6, 10, 15, \dots$?

    $21$. These are triangular numbers, formed by adding the next integer to the previous term.

16. What is the predicted value after $4$ hours if a tank fills at $5$ L per hour starting from $10$ L?

    $30$ L. The tank fills linearly at 5 L per hour, so add $5 \times 4$ to the initial 10 L.

17. What is the common difference in the arithmetic sequence $4, 7, 10, 13, \dots$?

    $3$. The common difference is found by subtracting consecutive terms in the arithmetic sequence, consistently yielding 3.

18. What is the next term in the sequence $1, 2, 4, 7, 11, \dots$?

    $16$. The differences increase by 1 each time, so add 5 to the last term.

19. What is the next term in the sequence $2, 4, 7, 11, 16, \dots$?

    $22$. The differences increase by 1 each time, so add 6 to the last term.

20. What is the next term in the arithmetic sequence $4, 7, 10, 13, \dots$?

    $16$. Add the common difference of 3 to the last term to find the next in the arithmetic sequence.

21. What is the next term in the geometric sequence $3, 6, 12, 24, \dots$?

    $48$. Multiply the last term by the common ratio of 2 to obtain the next term in the geometric sequence.

22. What is the next term in the sequence $2, 6, 18, 54, \dots$?

    $162$. This geometric sequence has a common ratio of 3, so multiply the last term by 3.

23. What is the next term in the sequence $20, 17, 13, 8, \dots$?

    $2$. The differences decrease by 1 each time, becoming more negative, so subtract 6 from the last term.

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