**1. Determine the next number in the sequence. 5, 13, 21, 29, __**

- 37
- 38
- 39
- 42
- 43

**2. Write a sequence of five consecutive even numbers that add to 60.**

- 6, 8, 10, 12, 14
- 8, 10, 12, 14, 16
- 9, 10, 11, 12, 13
- 10, 11, 12, 13, 14
- 10, 12, 14, 16, 18

**3. Determine the next number in the sequence.**

**4. The first two numbers in the Fibonacci sequence are 0 and 1. After that, each number is the sum of the previous two. Write the first six numbers in the Fibonacci sequence.**

- 0, 1, 1, 2, 2, 4
- 0, 1, 1, 2, 3, 4
- 0, 1, 1, 2, 3, 5
- 0, 1, 2, 3, 5, 8
- 0, 1, 2, 3, 6, 9

**5. Write the first six numbers in a sequence in which every number is three times the previous number and the first number is 2.**

- 2, 4, 8, 16, 32, 64
- 2, 4, 12, 32, 96, 288
- 2, 6, 12, 24, 72, 216
- 2, 6, 12, 36, 108, 324
- 2, 6, 18, 54, 162, 486

**6. Write a sequence of five consecutive even numbers that add to 0.**

- -4, -2, 0, 2, 4
- -3, -1, 1, 3, 5
- -2, 0, 2, 4, 6
- -2, -1, 0, 1, 2
- 0, 2, 4, 6, 8

**7. Find the 23rd term in the sequence below. 9, 15, 21, 27, 33, …**

- 135
- 136
- 138
- 141
- 142

**8. Write the next four numbers in the sequence below. 32, 48, 72, 108, …**

**9. Determine the next number in the sequence. 0, 1, 3, 6, 10, __**

- 13
- 14
- 15
- 16
- 17

**10. Find the 31st term in the sequence below. 69, 60, 51, 42, 33, …**

- -279
- -201
- -189
- -188
- -31

## Answer Key

**1. A.** Examine the sequence to find a pattern. The pattern is that every number is eight more than the last. Add to find the next number.

29 + 8 = 37

**2. B.** A sequence of five consecutive even numbers is a sequence of even numbers such that the difference between one number and the next is always 2. Here are some examples:

0, 2, 4, 6, 8

12, 14, 16, 18, 20

100, 102, 104, 106, 108

One way to find the correct sequence is to set up and solve an equation. If x represents the first term, subsequent terms are *x* + 2, *x* + 4, *x* + 6, and *x* + 8. The sum of all the terms is 60, so

x+ (x+ 2) + (x+ 4) + (x+ 6) + (x+ 8) = 605

x+ 20 = 605

x= 40

x= 8

Therefore, the sequence is 8, 10, 12, 14, 16.

**3. B.** Examine the sequence to find a pattern. The pattern is that every number is half of the previous number. Multiply by to find the next number.

**4. C.** As the problem states, the first two numbers are 0 and 1. Add them to find the third number in the Fibonacci sequence.

0 + 1 = 1

Continue this process of adding consecutive terms in the sequence to find the next three numbers in the sequence.

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

Therefore, the first six numbers in the Fibonacci sequence are 0, 1, 1, 2, 3, 5.

**5. E.** As the problem states, the first number is 2. To find the second number, multiply 2 by 3.

2 x 3 = 6

Continue this process of multiplying by 3 to find the next four numbers in the sequence.

6 x 3 = 18

18 x 3 = 54

54 x 3 = 162

162 x 3 = 486

Therefore, the first six numbers in the sequence are 2, 6, 18, 54, 162, 486.

**6. A.** A sequence of five consecutive even numbers is a sequence of even numbers such that the difference between one number and the next is always 2. Here are some examples:

0, 2, 4, 6, 8

12, 14, 16, 18, 20

100, 102, 104, 106, 108

If all of the numbers in a sequence are positive, then the sum of the sequence will also be positive. Therefore, in order for the sum to be zero, half of the numbers must be negative. In particular, for every positive number in the sequence is a corresponding negative number. Thus, the sequence should be -4, -2, 0, 2, 4.

**7. D.** Examine the sequence to find a pattern. The pattern is that every number is six more than the last. Thus, a straightforward way to calculate the 23rd term is to write out the first 23 terms in the sequence, but this would be very tedious. A much easier method is to find a formula *f*(*n*) for the *n*th number in the sequence and then plug in 23 for *n*.

Since each number is six more than the last, the formula will be something like *f*(*n*)=6*n*. However, notice that this formula is off by 3 for every number in the given sequence. Fix this by simply adding 3 in the formula. The result is *f*(*n*) = 6*n* + 3, which works for every value of *n*. Substitute 23 for *n* in this formula and calculate.

f(23) = 6(23) + 3= 138 + 3

= 141

**8. C.** Examine the sequence to find a pattern. The pattern is that every number is times the previous number. Multiply 108 by to find the next number in the sequence.

Continue multiplying to find the next three numbers in the sequence.

Therefore, the next four numbers are 162, 243, , .

**9. C.** Examine the sequence to find a pattern. Calculate the difference between consecutive numbers.

(2nd number) – (1st number) = 1 – 0 = 1

(3rd number) – (2nd number) = 3 – 1 = 2

(4th number) – (3rd number) = 6 – 3 = 3

(5th number) – (4th number) = 10 – 6 = 4

Therefore, the next number will be 5 more than the last number.

10 + 5 = 15

**10. B.** Examine the sequence to find a pattern. The pattern is that every number is nine less than the previous number. Thus, a straightforward way to calculate the 31st term is to write out the first 31 terms in the sequence, but this would be very tedious. A much easier method is to find a formula *f*(*n*) for the *n*th number in the sequence and then plug in 31 for *n*.

Since each number is nine less than the last, the formula will be something like *f*(*n*)=-9*n*. However, notice that this formula is off by 78 for every number in the given sequence. Fix this by simply adding 78 in the formula. The result is *f*(*n*) = -9*n* + 78, which works for every value of*n*. To answer the question, substitute 31 for *n* in this formula and calculate.