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Geometric Sequences — Easy Worksheet 2
Grade 9 · Whoobee Name: ____________________ Date: __________
Answer each question. Write rules in the form a_n = a(r)^(n - 1), for example a_n = 3(2)^(n - 1).
How to solve
In a geometric sequence you multiply by the same number r (the common ratio) each time. Find r by dividing any term by the term before it. The nth term is a_n = a_1(r)n-1.
Example
Find the common ratio of the geometric sequence 6, 12, 24, 48, ...
Answer: 2
Not quite. The answer is
💡 Divide each term by the one before it: 10 ÷ 5 = 2, 20 ÷ 10 = 2 and 40 ÷ 20 = 2. The ratio is always the same, so the common ratio is 2.
✓ Correct!
Not quite. The answer is
💡 Divide each term by the one before it: 10 ÷ 5 = 2, 20 ÷ 10 = 2 and 40 ÷ 20 = 2. The ratio is always the same, so the common ratio is 2.
💡 How to solve: Geometric Sequences
In a geometric sequence you multiply by the same number r (the common ratio) each time. Find r by dividing any term by the term before it. The nth term is a_n = a_1(r)n-1.
Try a similar one
Find the common ratio of the geometric sequence 3, 6, 12, 24, ...
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Find the common ratio: 10 ÷ 5 = 2, so each term is 2 times the one before. Multiply the 4th term by 2: 40 × 2 = 80. The next term is 80.
✓ Correct!
Not quite. The answer is
💡 Find the common ratio: 10 ÷ 5 = 2, so each term is 2 times the one before. Multiply the 4th term by 2: 40 × 2 = 80. The next term is 80.
💡 How to solve: Geometric Sequences
In a geometric sequence you multiply by the same number r (the common ratio) each time. Find r by dividing any term by the term before it. The nth term is a_n = a_1(r)n-1.
Try a similar one
Find the common ratio of the geometric sequence 6, 24, 96, 384, ...
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The differences are 5, 10, 20 and 40, not all the same, so it is not arithmetic. Divide each term by the one before: the ratios are all 2, so the sequence is geometric.
✓ Correct!
Not quite. The answer is
💡 The differences are 5, 10, 20 and 40, not all the same, so it is not arithmetic. Divide each term by the one before: the ratios are all 2, so the sequence is geometric.
💡 How to solve: Geometric Sequences
In a geometric sequence you multiply by the same number r (the common ratio) each time. Find r by dividing any term by the term before it. The nth term is a_n = a_1(r)n-1.
Try a similar one
Find the common ratio of the geometric sequence 3, 6, 12, 24, ...
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Divide each term by the one before it: 8 ÷ 2 = 4, 32 ÷ 8 = 4 and 128 ÷ 32 = 4. The ratio is always the same, so the common ratio is 4.
✓ Correct!
Not quite. The answer is
💡 Divide each term by the one before it: 8 ÷ 2 = 4, 32 ÷ 8 = 4 and 128 ÷ 32 = 4. The ratio is always the same, so the common ratio is 4.
💡 How to solve: Geometric Sequences
In a geometric sequence you multiply by the same number r (the common ratio) each time. Find r by dividing any term by the term before it. The nth term is a_n = a_1(r)n-1.
Try a similar one
Find the common ratio of the geometric sequence 2, 6, 18, 54, ...
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Divide each term by the one before it: 9 ÷ 3 = 3, 27 ÷ 9 = 3 and 81 ÷ 27 = 3. The ratio is always the same, so the common ratio is 3.
✓ Correct!
Not quite. The answer is
💡 Divide each term by the one before it: 9 ÷ 3 = 3, 27 ÷ 9 = 3 and 81 ÷ 27 = 3. The ratio is always the same, so the common ratio is 3.
💡 How to solve: Geometric Sequences
In a geometric sequence you multiply by the same number r (the common ratio) each time. Find r by dividing any term by the term before it. The nth term is a_n = a_1(r)n-1.
Try a similar one
Find the common ratio of the geometric sequence 5, 10, 20, 40, ...
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Find the common ratio: 12 ÷ 4 = 3, so each term is 3 times the one before. Multiply the 4th term by 3: 108 × 3 = 324. The next term is 324.
✓ Correct!
Not quite. The answer is
💡 Find the common ratio: 12 ÷ 4 = 3, so each term is 3 times the one before. Multiply the 4th term by 3: 108 × 3 = 324. The next term is 324.
💡 How to solve: Geometric Sequences
In a geometric sequence you multiply by the same number r (the common ratio) each time. Find r by dividing any term by the term before it. The nth term is a_n = a_1(r)n-1.
Try a similar one
Find the common ratio of the geometric sequence 3, 6, 12, 24, ...
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract each term from the next: the differences are 2, 2, 2 and 2. They are all the same, so the sequence is arithmetic.
✓ Correct!
Not quite. The answer is
💡 Subtract each term from the next: the differences are 2, 2, 2 and 2. They are all the same, so the sequence is arithmetic.
💡 How to solve: Geometric Sequences
In a geometric sequence you multiply by the same number r (the common ratio) each time. Find r by dividing any term by the term before it. The nth term is a_n = a_1(r)n-1.
Try a similar one
Find the common ratio of the geometric sequence 2, 4, 8, 16, ...
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Divide each term by the one before it: 20 ÷ 5 = 4, 80 ÷ 20 = 4 and 320 ÷ 80 = 4. The ratio is always the same, so the common ratio is 4.
✓ Correct!
Not quite. The answer is
💡 Divide each term by the one before it: 20 ÷ 5 = 4, 80 ÷ 20 = 4 and 320 ÷ 80 = 4. The ratio is always the same, so the common ratio is 4.
💡 How to solve: Geometric Sequences
In a geometric sequence you multiply by the same number r (the common ratio) each time. Find r by dividing any term by the term before it. The nth term is a_n = a_1(r)n-1.
Try a similar one
Find the common ratio of the geometric sequence 5, 10, 20, 40, ...
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Geometric Sequences — Easy Worksheet 2
Answer each question. Write rules in the form a_n = a(r)^(n - 1), for example a_n = 3(2)^(n - 1).