Determine the indicated term in the given sequence.
-The 7 th term of $1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \ldots$
A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 729 }$
C) $\frac { 1 } { 6561 }$
D) $\frac { 1 } { 243 }$

Question

Quizplus · Accepted Answer

The sequence is a geometric sequence with the first term $a = 1$ and common ratio $r = \frac{1}{3}$. The $n$th term of a geometric sequence is given by $a_n = a \cdot r^{(n-1)}$. For the 7th term, $n = 7$, so $a_7 = 1 \cdot (\frac{1}{3})^{(7-1)} = \frac{1}{729}$.

Determine the Indicated Term in the Given Sequence 1,13,19,…1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \ldots1,31​,91​,…

Determine the Indicated Term in the Given Sequence $1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \ldots$