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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, each term after the first is obtained by multiplying the previous term by a constant number, which suggests that the sequence is geometric.
- Find Common Ratio: Determine the common ratio of the sequence.To find the common ratio, divide the second term by the first term, or the third term by the second term. and Common Ratio:
- Calculate Next Term: Calculate the next term in the sequence using the common ratio.The last term given in the sequence is . To find the next term, multiply the last term by the common ratio.
- Verify Result: Verify the result to ensure there are no mathematical errors.The sequence follows a pattern of multiplication by . The progression from to (), and from to (), correctly leads to the next term being , which is .
