Find the indicated term(s) of the given sequence.
-The general term of the sequence $3 , \frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \ldots$
A) $a _ { n } = 3 \left( \frac { 1 } { 2 } \right) ^ { n }$
B) $a _ { n } = 3 \left( \frac { 1 } { 2 } \right) ^ { n + 1 }$
C) $a _ { n } = 3 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$
D) $a _ { n } = 3 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The sequence is a geometric sequence with the first term $a_1 = 3$ and common ratio $r = \frac{1}{2}$. The general term of a geometric sequence is given by $a_n = a_1 \cdot r^{n-1}$. Substituting $a_1 = 3$ and $r = \frac{1}{2}$ gives $a_n = 3 \left( \frac{1}{2} \right)^{n-1}$, which matches option C.

Find the Indicated Term(s) of the Given Sequence 3,32,34,38,316,…3 , \frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \ldots3,23​,43​,83​,163​,…

Find the Indicated Term(s) of the Given Sequence $3 , \frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \ldots$