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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 Sequence Type: Identify whether the given sequence is geometric or arithmetic.In the given sequence, consecutive terms seem to have a common ratio because each term is smaller than the previous one by a consistent factor.
- Find Common Ratio: Identify the common ratio.Two consecutive terms are and .Common Ratio:
- Calculate Next Term: Find the next term in the sequence.The last term given in the sequence is .To find the next term, multiply the last term by the common ratio.
- Check Result Consistency: Check the result for consistency with the sequence.The sequence is , , , and if we have done our calculations correctly, the next term should be .To check, we can see if is five times smaller than , and if is five times smaller than . and , which is consistent with our result.
