Find the general term, $a_n$, of the given geometric sequence
-$\frac{1}{6}, \frac{1}{2}, \frac{3}{2}, \ldots$

A) $a_{n}=\frac{1}{6}+\frac{1}{3}(n-1)$

B) $\mathrm{a}_{\mathrm{n}}=\frac{1}{6}+3(\mathrm{n}-1)$

C) $a_{n}=\frac{1}{6}(3)^{n-1}$

D) $a_{n}=\left(\frac{1}{6}\right)^{n-1}+\frac{1}{3}$

Question

Find the general term, $a_n$, of the given geometric sequence
-$\frac{1}{6}, \frac{1}{2}, \frac{3}{2}, \ldots$

A) $a_{n}=\frac{1}{6}+\frac{1}{3}(n-1)$

B) $\mathrm{a}_{\mathrm{n}}=\frac{1}{6}+3(\mathrm{n}-1)$

C) $a_{n}=\frac{1}{6}(3)^{n-1}$

D) $a_{n}=\left(\frac{1}{6}\right)^{n-1}+\frac{1}{3}$

Quizplus · Accepted Answer

The given sequence is a geometric sequence where each term is multiplied by 3 to get the next term. The first term $a_1 = \frac{1}{6}$, and the common ratio $r = 3$. The general term of a geometric sequence is given by $a_n = a_1 \cdot r^{n-1}$, which in this case is $a_n = \frac{1}{6} \cdot 3^{n-1}$.

Find the General Term ana_nan​ , of the Given Geometric Sequence -

Find the General Term $a_n$ , of the Given Geometric Sequence
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