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). 150,120,96,dots Find the 6th term. Answer:

Question

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).  150,120,96,dots Find the 6th term. Answer:

Bytelearn · Accepted Answer

Identify Pattern: Identify the pattern in the sequence. We need to determine the pattern by which the sequence is generated. By looking at the given terms, we can see that each term is a certain percentage of the previous term. $120 is \frac{120}{150} = 0.8$ (or 80%) of $150. $96 is \frac{96}{120} = 0.8$ (or 80%) of $120. This suggests that each term is 80% of the previous term, which means the sequence is a geometric sequence with a common ratio of 0.8.Use Formula: Use the formula for the nth term of a geometric sequence. The nth term of a geometric sequence can be found using the formula $a_n = a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number. Here, $a_1 = 150$, $r = 0.8$, and we want to find the 6th term, so $n = 6$.Calculate 6th Term: Calculate the 6th term. Using the formula, we calculate the 6th term as follows: $a_6 = 150 \cdot 0.8^{(6-1)}$ $a_6 = 150 \cdot 0.8^5$ $a_6 = 150 \cdot 0.32768$ $a_6 = 49.152$Round Answer: Round the answer to the nearest thousandth. The 6th term, when rounded to the nearest thousandth, is: $a_6 \approx 49.152$ Since 49.152 is already to the nearest thousandth, we do not need to round further.

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). $\newline$ $150,120,96, \ldots$ $\newline$ Find the $6$ th term. $\newline$ Answer:

Full solution

More problems from Powers with decimal bases

Related topics

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).\newline150,120,96,… 150,120,96, \ldots 150,120,96,…\newlineFind the 666th term.\newlineAnswer:

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). $\newline$ $150,120,96, \ldots$ $\newline$ Find the $6$ th term. $\newline$ Answer: