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). 6,2,(2)/(3),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).  6,2,(2)/(3),dots Find the 6th term. Answer:

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Identify Pattern: Identify the pattern in the sequence. The sequence given is 6, 2, 2/3, ... To find the pattern, we look at how each term is related to the previous one. We divide each term by 3 to get the next term. 6 ÷ 3 = 2 2 ÷ 3 = 2/3 This is a geometric sequence with a common ratio of 1/3.Use Formula: Use the formula for the nth term of a geometric sequence. The nth term of a geometric sequence is given by the formula: a_n = a_1 * r^(n-1) where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.Plug in Values: Plug in the values to find the 6th term. a_1 = 6 (the first term) r = 1/3 (the common ratio) n = 6 (we want to find the 6th term) a_6 = 6 * (1/3)^(6-1) a_6 = 6 * (1/3)^5Calculate 6th Term: Calculate the 6th term. a_6 = 6 * (1/3)^5 a_6 = 6 * (1/243) a_6 = 6/243 a_6 = 2/81Convert to Decimal: Convert the fraction to a decimal and round to the nearest thousandth if necessary. 2/81 as a decimal is approximately 0.0247 Rounded to the nearest thousandth, it is 0.025.

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). $\newline$ $6,2, \frac{2}{3}, \ldots$ $\newline$ Find the $6$ th term. $\newline$ 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). $\newline$ $6,2, \frac{2}{3}, \ldots$ $\newline$ Find the $6$ th term. $\newline$ Answer: