we will check each options
we know that
geometric sequence are sequences whose common ratios are same
graph-A:
we are given terms as
[tex]a_1=1[/tex]
[tex]a_2=3[/tex]
[tex]a_3=5[/tex]
[tex]a_4=7[/tex]
[tex]a_5=9[/tex]
now, we can find common ratios
[tex]r_1=\frac{a_2}{a_1}[/tex]
[tex]r_1=\frac{3}{1}[/tex]
[tex]r_1=3[/tex]
[tex]r_2=\frac{a_3}{a_2}[/tex]
[tex]r_2=\frac{5}{3}[/tex]
we can see that r1 is not equal to r2
so, this is not geometric sequnce
graph-B:
we are given terms as
[tex]a_1=1[/tex]
[tex]a_2=2[/tex]
[tex]a_3=4[/tex]
[tex]a_4=8[/tex]
[tex]a_5=9[/tex]
now, we can find common ratios
[tex]r_1=\frac{a_2}{a_1}[/tex]
[tex]r_1=\frac{2}{1}[/tex]
[tex]r_1=2[/tex]
[tex]r_2=\frac{a_3}{a_2}[/tex]
[tex]r_2=\frac{4}{2}[/tex]
[tex]r_2=2[/tex]
[tex]r_3=\frac{a_4}{a_3}[/tex]
[tex]r_3=\frac{8}{4}[/tex]
[tex]r_3=2[/tex]
so,
[tex]r_1=r_2=r_3=2[/tex]
so, this is geometric sequnce
graph-C:
we are given terms as
[tex]a_1=2[/tex]
[tex]a_4=4[/tex]
[tex]a_9=6[/tex]
since, they are not in proper sequence
so, this is not geometric sequence
graph-D:
we are given terms as
[tex]a_1=1[/tex]
[tex]a_2=4[/tex]
[tex]a_3=9[/tex]
now, we can find common ratios
[tex]r_1=\frac{a_2}{a_1}[/tex]
[tex]r_1=\frac{4}{1}[/tex]
[tex]r_1=4[/tex]
[tex]r_2=\frac{a_3}{a_2}[/tex]
[tex]r_2=\frac{9}{4}[/tex]
Since, r1 is not equal to r2
so, this is not geometric sequence.........Answer
