Determine Sequence Pattern - International Brotherhood of Electrical Workers Exam IBEW

1. What is the next number in the sequence of primes $2, 3, 5, 7, 11, \dots$?

   $13$. This sequence lists prime numbers in order, so identify the next prime after $11$.

2. What is the next number in the pattern "multiply by $3$ then subtract $1$": $2, 5, 14, 41, \dots$?

   $122$. The pattern multiplies by $3$ and subtracts $1$ each time, so apply to the last term.

3. What is the next number in the square-number sequence $1, 4, 9, 16, 25, \dots$?

   $36$. This sequence consists of perfect squares ($1^2, 2^2, 3^2, \dots$), so square the next integer $6$.

4. What is the next number in the alternating pattern "$\times 2$, then $+3$": $1, 2, 5, 10, 13, \dots$?

   $26$. The pattern alternates multiplying by $2$ and adding $3$, so multiply the last term by $2$.

5. What is the next number when the pattern is "add consecutive odd numbers": $2, 3, 6, 11, 18, \dots$?

   $27$. The pattern adds consecutive odd numbers starting from $1$, so add $9$ to the last term.

6. What is the next number in the sequence of multiples of $6$: $6, 12, 18, 24, \dots$?

   $30$. This sequence lists multiples of $6$, so add $6$ to the last term.

7. What is the next number in the sequence of powers of $2$: $2, 4, 8, 16, 32, \dots$?

   $64$. This sequence represents powers of $2$ ($2^1, 2^2, \dots$), so compute $2^6$.

8. What is the next number in the triangular-number sequence $1, 3, 6, 10, 15, \dots$?

   $21$. This triangular number sequence sums the first $n$ natural numbers, so add $6$ to the last term.

9. What is the next number in the alternating sequence $9, 1, 8, 2, 7, 3, \dots$?

   $6$. The sequence interleaves a decreasing series ($9,8,7,\dots$) with an increasing one ($1,2,3,\dots$), so continue the decreasing pattern.

10. What is the next number when the pattern is "add consecutive integers": $4, 5, 7, 10, 14, \dots$?

    $19$. The pattern adds consecutive integers starting from $1$, so add $5$ to the last term.

11. What is the next number in the sequence "multiply by $-2$": $3, -6, 12, -24, \dots$?

    $48$. The pattern multiplies by $-2$ each time, alternating signs, so multiply the last term by $-2$.

12. What is the next number in the alternating pattern "$+5$, then $\times 2$": $2, 7, 14, 19, 38, \dots$?

    $43$. The pattern alternates adding $5$ and multiplying by $2$, so add $5$ to the last term.

13. What is the next number in the sequence "$\times 2$, $\times 3$, $\times 2$, $\times 3$": $1, 2, 6, 12, 36, \dots$?

    $72$. The pattern alternates multiplying by $2$ and $3$, so multiply the last term by $2$.

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

    $48$. This geometric sequence multiplies by a common ratio of $2$, so multiply the last term by $2$.

15. What is the next number in the arithmetic sequence $50, 45, 40, 35, \dots$?

    $30$. This arithmetic sequence decreases by a common difference of $5$, so subtract $5$ from the last term.

16. What is the next number in the pattern "multiply by $2$ then add $1$": $1, 3, 7, 15, \dots$?

    $31$. The pattern multiplies by $2$ and adds $1$ each time, so apply to the last term.

17. What is the next number in the geometric sequence $160, 80, 40, 20, \dots$?

    $10$. This geometric sequence multiplies by a common ratio of $\frac{1}{2}$, so halve the last term.

18. What is the next number in the Fibonacci-type sequence $1, 1, 2, 3, 5, 8, \dots$?

    $13$. This Fibonacci sequence forms each term by summing the two preceding ones, so add the last two terms.

19. What is the next number in the cube-number sequence $1, 8, 27, 64, \dots$?

    $125$. This sequence consists of perfect cubes ($1^3, 2^3, 3^3, \dots$), so cube the next integer $5$.

20. What is the next number in the arithmetic sequence $7, 11, 15, 19, \dots$?

    $23$. This arithmetic sequence increases by a common difference of $4$, so add $4$ to the last term to find the next.

21. What is the next number when the differences double: $2, 5, 11, 23, \dots$?

    $47$. The differences double each time ($3, 6, 12, \dots$), so add $24$ to the last term.

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