Geometric sequence term
A geometric sequence is a sequence where each term is obtained by multiplying the previous term by the same constant ratio. To find a specific term, you usually need the first term and the common ratio.
Method
- Identify the first term and the common ratio. The ratio is the number you multiply by each time to move from one term to the next.
- Use repeated multiplication to reach the requested term, or use the pattern of powers of the ratio.
- Simplify your result carefully. If the terms involve fractions or negative numbers, keep track of signs and reduce the final expression.
Example of the process
If the sequence starts with a term and each new term is found by multiplying by the same number, continue that multiplication the needed number of times until you reach the target position.
Check your answer
- Divide one term by the previous term to see whether the ratio stays constant.
- Make sure your answer matches the expected sign and size of the sequence.
- If possible, verify by substituting your term back into the pattern.
When the exercise asks for the term of a geometric sequence, the key idea is consistency: every step should use the same multiplier.