Skills · Functions · Sequences

Writing a geometric 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, 6, 12, 24, …
• from the first term and the ratio: a1 = 5, r = 3
• from a list with a fraction ratio: 80, 40, 20, 10, …

Sample Sheet · Level 1

1. a₁ = 10, r = 3: rule for a_n
2. a₁ = 2, r = 4: rule for a_n
3. a₁ = 4, r = 6: rule for a_n
4. a₁ = 5, r = 6: rule for a_n
5. 7, 21, 63, 189, …: rule for a_n
6. 2, 6, 18, 54, …: rule for a_n
7. 8, 16, 32, 64, …: rule for a_n
8. 5, 20, 80, 320, …: rule for a_n

Answer key

1. a_n = 10(3)^{n − 1}
2. a_n = 2(4)^{n − 1}
3. a_n = 4(6)^{n − 1}
4. a_n = 5(6)^{n − 1}
5. a_n = 7(3)^{n − 1}
6. a_n = 2(3)^{n − 1}
7. a_n = 8(2)^{n − 1}
8. a_n = 5(4)^{n − 1}

Sample Sheet · Level 3

1. a₁ = 11, r = 3: rule for a_n
2. a₁ = 12, r = 2: rule for a_n
3. a₁ = 14, r = 5: rule for a_n
4. 48, 24, 12, 6, …: rule for a_n
5. 7, 35, 175, 875, …: rule for a_n
6. 12, 48, 192, 768, …: rule for a_n
7. 32, 16, 8, 4, …: rule for a_n
8. 108, 36, 12, 4, …: rule for a_n

Answer key

1. a_n = 11(3)^{n − 1}
2. a_n = 12(2)^{n − 1}
3. a_n = 14(5)^{n − 1}
4. a_n = 48(12)^{n − 1}
5. a_n = 7(5)^{n − 1}
6. a_n = 12(4)^{n − 1}
7. a_n = 32(12)^{n − 1}
8. a_n = 108(13)^{n − 1}

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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