Provide an appropriate response.
-Find the 11 th term of the geometric sequence whose first term is 3000 and whose common ratio is $\frac { 1 } { 3 }$.
A) $\frac { 1000 } { 19683 }$
B) $\frac { 1000 } { 177147 }$
C) $\frac { 9010 } { 3 }$
D) $\frac { 1000 } { 59049 }$

Question

Quizplus · Accepted Answer

The 11th term of a geometric sequence is given by the formula:$$a_{11} = a_1 \cdot r^{11-1}$$where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number.In this case, $a_1 = 3000$ and $r = \frac{1}{3}$. Substituting these values into the formula, we get:$$a_{11} = 3000 \cdot \left(\frac{1}{3}\right)^{11-1}$$$$a_{11} = 3000 \cdot \left(\frac{1}{3}\right)^{10}$$$$a_{11} = 3000 \cdot \frac{1}{59049}$$$$a_{11} = \frac{1000}{19683}$$Therefore, the correct answer is A.

Provide an Appropriate Response 13\frac { 1 } { 3 }31​

Provide an Appropriate Response $\frac { 1 } { 3 }$