The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary). 9,6,4,dots Find the 6th term. Answer:

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The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).  9,6,4,dots Find the 6th term. Answer:

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Identify Pattern: Identify the pattern in the sequence. The given sequence is 9, 6, 4, ... To find the pattern, we look at the differences between consecutive terms. The difference between the first and second term is 6 - 9 = -3. The difference between the second and third term is 4 - 6 = -2. The differences are not constant, so this is not an arithmetic sequence. We need to look for another type of pattern, such as a geometric sequence or a sequence with a varying difference.Check Geometric Sequence: Check for a geometric sequence. A geometric sequence is one where each term after the first is found by multiplying the previous term by a constant called the common ratio (r). To find the common ratio, we divide the second term by the first term and the third term by the second term. The common ratio between the second and first term is 6 / 9 = 2/3. The common ratio between the third and second term is 4 / 6 = 2/3. Since the common ratio is the same for these terms, we can conclude that this is a geometric sequence with a common ratio of 2/3.Use nth Term Formula: Use the formula for the nth term of a geometric sequence to find the 6th term. The formula for the nth term (a_n) of a geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. The first term (a_1) is 9, the common ratio (r) is 2/3, and we want to find the 6th term (n=6). So, a_6 = 9 * (2/3)^(6-1) = 9 * (2/3)^5.Calculate 6th Term: Calculate the 6th term. a_6 = 9 * (2/3)^5 a_6 = 9 * (32/243) (since 2^5 = 32 and 3^5 = 243) a_6 = 288/243 a_6 ≈ 1.185 Since we need to round to the nearest thousandth, the 6th term is approximately 1.185.

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary). $\newline$ $9,6,4, \ldots$ $\newline$ Find the $6$ th term. $\newline$ Answer:

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