Given sequence:
1234, 123.4, 12.34, 1.234
Let us check the ratios between the consecutive two terms whether same or not.
[tex]\begin{gathered} r_1=\frac{a_2}{a_1} \\ =\frac{123.4}{1234} \\ =\frac{1}{10} \end{gathered}[/tex][tex]\begin{gathered} r_2=\frac{a_3}{a_2} \\ =\frac{12.34}{123.4} \\ =\frac{1}{10} \end{gathered}[/tex]Similarly, we get
[tex]r_3=\frac{1}{10}[/tex]Since, the given sequence is having the common ratio.
Therefore, the given sequence is geometric sequence.
