Identifying Sentence Errors Practice Questions

Use these Sequences practice questions to review arithmetic sequences, geometric sequences, Fibonacci sequences, consecutive even numbers, sequence patterns, and nth-term formulas. After answering each question, open the explanation to see the step-by-step solution.

Sequences Topics Covered

  • Finding the next term in a sequence
  • Recognizing arithmetic patterns
  • Recognizing geometric patterns
  • Working with consecutive even numbers
  • Using the Fibonacci sequence
  • Finding nth terms
  • Writing sequence formulas

Sequences Practice Questions

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

  1. 37
  2. 38
  3. 39
  4. 42
  5. 43
Show Answer

Answer: A. 37

Look at the difference between each pair of consecutive terms.

13 − 5 = 8

21 − 13 = 8

29 − 21 = 8

Each term is 8 more than the previous term, so add 8 to 29.

29 + 8 = 37

The next number is 37.

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

  1. 6, 8, 10, 12, 14
  2. 8, 10, 12, 14, 16
  3. 9, 10, 11, 12, 13
  4. 10, 11, 12, 13, 14
  5. 10, 12, 14, 16, 18
Show Answer

Answer: B. 8, 10, 12, 14, 16

Five consecutive even numbers increase by 2 each time.

Let x represent the first number. Then the five numbers are:

x, x + 2, x + 4, x + 6, x + 8

Their sum is 60:

x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 60

5x + 20 = 60

5x = 40

x = 8

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

3. Determine the next number in the sequence.

6, 3,
32,
34,
__

  1. 14
  2. 38
  3. 37
  4. 12
  5. 32
Show Answer

Answer: B. 38

Each number is half of the previous number.

6 ÷ 2 = 3

3 ÷ 2 =
32

32
÷ 2 =
34

Now multiply the last term by one-half:


34
×
12
=
38

The next number is 38.

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.

  1. 0, 1, 1, 2, 2, 4
  2. 0, 1, 1, 2, 3, 4
  3. 0, 1, 1, 2, 3, 5
  4. 0, 1, 2, 3, 5, 8
  5. 0, 1, 2, 3, 6, 9
Show Answer

Answer: C. 0, 1, 1, 2, 3, 5

The first two numbers are 0 and 1.

Add them to find the third number:

0 + 1 = 1

Continue adding consecutive terms:

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

The first six numbers are 0, 1, 1, 2, 3, 5.

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.

  1. 2, 4, 8, 16, 32, 64
  2. 2, 4, 12, 32, 96, 288
  3. 2, 6, 12, 24, 72, 216
  4. 2, 6, 12, 36, 108, 324
  5. 2, 6, 18, 54, 162, 486
Show Answer

Answer: E. 2, 6, 18, 54, 162, 486

The first number is 2. Each number after that is three times the previous number.

2 × 3 = 6

6 × 3 = 18

18 × 3 = 54

54 × 3 = 162

162 × 3 = 486

The first six numbers are 2, 6, 18, 54, 162, 486.

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

  1. −4, −2, 0, 2, 4
  2. −3, −1, 1, 3, 5
  3. −2, 0, 2, 4, 6
  4. −2, −1, 0, 1, 2
  5. 0, 2, 4, 6, 8
Show Answer

Answer: A. −4, −2, 0, 2, 4

Five consecutive even numbers increase by 2 each time.

The sequence must add to 0, so the positive and negative terms need to balance each other.

−4 + (−2) + 0 + 2 + 4 = 0

Therefore, the correct sequence is −4, −2, 0, 2, 4.

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

  1. 135
  2. 136
  3. 138
  4. 141
  5. 142
Show Answer

Answer: D. 141

The sequence increases by 6 each time, so it is an arithmetic sequence.

The first term is 9, and the common difference is 6.

A formula for the nth term is:

f(n) = 6n + 3

Substitute 23 for n:

f(23) = 6(23) + 3

f(23) = 138 + 3

f(23) = 141

The 23rd term is 141.

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

  1. 124, 140, 156, 172
  2. 4843,
    1354,
    4058,
    12,07281
  3. 162, 243,
    7292,
    21874
  4. 162, 324, 648, 1296
  5. 172, 258, 387, 581
Show Answer

Answer: C. 162, 243, 7292, 21874

Each number is multiplied by 32 to get the next term.


108 ×
32
= 162


162 ×
32
= 243


243 ×
32
=
7292


7292
×
32
=
21874

The next four numbers are 162, 243, 7292, and 21874.

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

  1. 13
  2. 14
  3. 15
  4. 16
  5. 17
Show Answer

Answer: C. 15

Look at the differences between consecutive terms:

1 − 0 = 1

3 − 1 = 2

6 − 3 = 3

10 − 6 = 4

The differences are increasing by 1 each time. The next difference should be 5.

10 + 5 = 15

The next number is 15.

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

  1. −279
  2. −201
  3. −189
  4. −188
  5. −31
Show Answer

Answer: B. −201

The sequence decreases by 9 each time, so it is an arithmetic sequence.

A formula for the nth term is:

f(n) = −9n + 78

Substitute 31 for n:

f(31) = −9(31) + 78

f(31) = −279 + 78

f(31) = −201

The 31st term is −201.

How to Use These Sequences Practice Questions

Start by answering each question before opening the explanation. Then compare your work to the step-by-step solution. If you miss a question, review the pattern or formula used in the solution before moving on.

For extra review, focus on the sequence types you miss most often. Some questions require recognizing a constant difference, while others require recognizing a constant multiplier, adding previous terms, or using a formula for the nth term.

 

Last Updated: July 3, 2026