Find the general term, $a_n$, of the given geometric sequence
-$36,6,1, \ldots$
A) $a_{n}=6(n-1)$
B) $a_{n}=6^{3-n}$
C) $a_{n}=6^{n}$
D) $a_{n}=6^{n-1}$

Question

Quizplus · Accepted Answer

The given sequence is a geometric sequence with the first term $a_1 = 36$ and a common ratio $r = \frac{1}{6}$. The general term of a geometric sequence is given by $a_n = a_1 \cdot r^{n-1}$. Substituting $a_1 = 36$ and $r = \frac{1}{6}$, we get $a_n = 36 \cdot (\frac{1}{6})^{n-1}$. Since $36 = 6^2$, we can rewrite this as $a_n = 6^2 \cdot 6^{-(n-1)} = 6^{2-(n-1)} = 6^{3-n}$.

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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