Continue a geometric sequence
The idea
Divide successive nonzero terms to check for a constant ratio.
Step by step
- Divide successive nonzero terms to check for a constant ratio.
- Multiply the final term by that common ratio to get the next term.
- Connect the rule to an = a1rn−1, counting the first term as n = 1.
Example
A sequence multiplies by the same positive factor each time: 2, 6, 18, 54, ___. What is the next term?
Answer
162
Each term is multiplied by 3. The next term is 54 × 3 = 162.
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5 questionsTry it together
Start with 3 and repeatedly double. Write the first five terms and explain why a linear rule will not fit them.
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