Skills · Functions · Sequences

Writing an arithmetic sequence’s rule

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

• from the list: 3, 7, 11, 15, …
• from the first term and the difference: a1 = 7, d = −3
• from a falling list: 40, 37, 34, 31, …
• from two terms: a4 = 10 and a9 = 25

Sample Sheet · Level 1

1. a₁ = 10, d = 5: rule for a_n
2. a₁ = 14, d = 2: rule for a_n
3. a₁ = 8, d = 3: rule for a_n
4. a₁ = 7, d = 6: rule for a_n
5. 10, 18, 26, 34, …: rule for a_n
6. 9, 17, 25, 33, …: rule for a_n
7. 7, 9, 11, 13, …: rule for a_n
8. 5, 12, 19, 26, …: rule for a_n

Answer key

1. a_n = 5n + 5
2. a_n = 2n + 12
3. a_n = 3n + 5
4. a_n = 6n + 1
5. a_n = 8n + 2
6. a_n = 8n + 1
7. a_n = 2n + 5
8. a_n = 7n − 2

Sample Sheet · Level 3

1. a₁ = 16, d = −2: rule for a_n
2. a₁ = −7, d = −9: rule for a_n
3. 13, 5, −3, −11, …: rule for a_n
4. −3, 4, 11, 18, …: rule for a_n
5. 35, 33, 31, 29, …: rule for a_n
6. −2, 1, 4, 7, …: rule for a_n
7. a₅ = −39 and a₁₀ = −84: rule for a_n
8. a₃ = 9 and a₅ = 27: rule for a_n

Answer key

1. a_n = −2n + 18
2. a_n = −9n + 2
3. a_n = −8n + 21
4. a_n = 7n − 10
5. a_n = −2n + 37
6. a_n = 3n − 5
7. a_n = −9n + 6
8. a_n = 9n − 18

Make your own

Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.

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