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Find the missing terms in the geometric sequence below.
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Q. Find the missing terms in the geometric sequence below.
- Identify Pattern: Identify the pattern in the geometric sequence.A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio . We are given the first term and the last term , and we need to find the common ratio and the missing terms.
- Calculate Common Ratio: Calculate the common ratio . Since we have the first term and the sixth term , we can use the formula for the nth term of a geometric sequence, which is , where is the term number. Here, we have . We can solve for by substituting and into the equation: To find , we take the fifth root of both sides:
- Find Missing Terms: Use the common ratio to find the missing terms.Now that we have the common ratio , we can find the missing terms by multiplying each term by the common ratio to get the next term.Second term: Third term: Fourth term: Fifth term:
- Verify Sequence: Verify the sequence.To ensure there are no mistakes, we can check that the fifth term multiplied by the common ratio gives us the sixth term:This is not equal to the sixth term () we were given, which means there is a mistake in our calculations.
