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Grade 9 · Math

Continue a geometric sequence

Recognize repeated multiplication and use a common ratio to extend a geometric sequence.

6 authored questions + worked example

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Worked example

A sequence multiplies by the same positive factor each time: 2, 6, 18, 54, ___. What is the next term?

Answer & why

Answer: 162

Each term is multiplied by 3. The next term is 54 × 3 = 162.

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All questions

All 6 authored questions for this skill.

Question 1

A sequence multiplies by the same positive factor each time: 4, 12, 36, 108, ___. What is the next term?

  1. 326
  2. 325
  3. 324
  4. 323
A hint

Find the constant ratio by dividing a term by the previous term.

Answer & why

Answer: 324

Each term is multiplied by 3. The next term is 108 × 3 = 324.

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Question 2

A sequence multiplies by the same positive factor each time: 5, 10, 20, 40, ___. What is the next term?

  1. 79
  2. 80
  3. 82
  4. 81
A hint

Find the constant ratio by dividing a term by the previous term.

Answer & why

Answer: 80

Each term is multiplied by 2. The next term is 40 × 2 = 80.

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Question 3

A sequence multiplies by the same positive factor each time: 2, 8, 32, 128, ___. What is the next term?

  1. 514
  2. 513
  3. 512
  4. 511
A hint

Find the constant ratio by dividing a term by the previous term.

Answer & why

Answer: 512

Each term is multiplied by 4. The next term is 128 × 4 = 512.

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Question 4

A sequence multiplies by the same positive factor each time: 6, 12, 24, 48, ___. What is the next term?

  1. 95
  2. 96
  3. 97
  4. 98
A hint

Find the constant ratio by dividing a term by the previous term.

Answer & why

Answer: 96

Each term is multiplied by 2. The next term is 48 × 2 = 96.

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Question 5

A sequence multiplies by the same positive factor each time: 2, 6, 18, 54, ___. What is the next term?

  1. 161
  2. 164
  3. 163
  4. 162
A hint

Find the constant ratio by dividing a term by the previous term.

Answer & why

Answer: 162

Each term is multiplied by 3. The next term is 54 × 3 = 162.

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Question 6

A sequence multiplies by the same positive factor each time: 3, 6, 12, 24, ___. What is the next term?

  1. 49
  2. 50
  3. 47
  4. 48
A hint

Find the constant ratio by dividing a term by the previous term.

Answer & why

Answer: 48

Each term is multiplied by 2. The next term is 24 × 2 = 48.

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