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What is the next term of the geometric sequence?
Full solution
Q. What is the next term of the geometric sequence?
- Identify pattern in sequence: Identify the pattern in the sequence to determine if it is geometric.The given sequence is . We need to check if there is a common ratio between the terms.
- Calculate common ratio: Calculate the common ratio by dividing the second term by the first term.Common ratio = = =
- Verify common ratio: Verify the common ratio by dividing the third term by the second term to ensure consistency.Common ratio check = Since the common ratio is consistent, we can confirm the sequence is geometric with a common ratio of .
- Find next term in sequence: Find the next term in the sequence by multiplying the last known term by the common ratio.Next term = $\(3\) \times \left(-\frac{\(4\)}{\(3\)}\right) = \(-4\)
