Answer
The given sequence is geometric sequence and the common ratio = $\frac{1}{2}$.
Work Step by Step
The given general term is $a_{n}$ = $(\frac{1}{2})^{n}$
First term $a_{1}$ = $(\frac{1}{2})$ (if n=1)
Second term $a_{2}$ = $(\frac{1}{2})^{2}$ = $(\frac{1}{4})$ (if n=2)
Third term $a_{3}$ = $(\frac{1}{2})^{3}$ = $(\frac{1}{8})$ (if n=3)
Forth term $a_{4}$ = $(\frac{1}{2})^{4}$ = $(\frac{1}{16})$ (if n=4)
Ratio of consecutive terms.
$\frac{(\frac{1}{16})}{(\frac{1}{8})}$ = $(\frac{1}{2})$.
$\frac{(\frac{1}{8})}{(\frac{1}{4})}$ = $(\frac{1}{2})$.
$\frac{(\frac{1}{4})}{(\frac{1}{2})}$ = $(\frac{1}{2})$.
From above we observe that the ratio of two consecutive terms is constant. So the given sequence is geometric sequence and the common ratio = $(\frac{1}{2})$.
