Property 2
Geometrical Sequence
\((a_n)\) is a sequence and for \(\forall n\in\mathbb N^+;\)
\(\samefrac{a_n}{a_{n-1}}=r\)
\((a_n)\) sequence is called geometric sequence
"\(r\)" is called common denominator.
if \((a_n)\) geometric sequence
\(a_n=a_1\cdot r^{n-1}\)
\(a_n=a_p\cdot r^{n-p}\)
\(a_n=\sqrt{a_{n-p}\cdot a_{n+p}}\)
\(S_n=a_1\cdot\samefrac{1-r^n}{1-r}\)
The sequences below are the geometrical sequence.
1.
\(\samefrac{a_5\cdot a_9}{a_3\cdot a_8}=8\)
\(\Rightarrow r=?\)
2.
\(r=\samefrac12\)
\(a_4=6\)
\(a_k=24\)
\(\Rightarrow k=?\)
3.
\(a_1=2\)
\(r=6\)
\(\Rightarrow a_n=?\)
4.
\(a_1=4\)
\(r=\samefrac18\)
\(\Rightarrow a_6=?\)
5.
\(a_3=1\)
\(a_7=\samefrac1{81}\)
\(\Rightarrow r=?\)
6.
\(a_1=2\)
\(a_6=64\)
\(\Rightarrow a_9=?\)
7.
\(a_1=\samefrac12\)
\(a_3=4\)
\(\Rightarrow r=?\)
8.
\(a_7+a_4=2(a_7-a_4)\)
\(\Rightarrow r=?\)