Question

50 points. Which graph represents a geometric sequence?

Answer 1

On ed the answer is B

Answer 2

we will check each options

we know that

geometric sequence are sequences whose common ratios are same

graph-A:

we are given terms as

$a_1=1$

$a_2=3$

$a_3=5$

$a_4=7$

$a_5=9$

now, we can find common ratios

$r_1=\frac{a_2}{a_1}$

$r_1=\frac{3}{1}$

$r_1=3$

$r_2=\frac{a_3}{a_2}$

$r_2=\frac{5}{3}$

we can see that r1 is not equal to r2

so, this is not geometric sequnce

graph-B:

we are given terms as

$a_1=1$

$a_2=2$

$a_3=4$

$a_4=8$

$a_5=9$

now, we can find common ratios

$r_1=\frac{a_2}{a_1}$

$r_1=\frac{2}{1}$

$r_1=2$

$r_2=\frac{a_3}{a_2}$

$r_2=\frac{4}{2}$

$r_2=2$

$r_3=\frac{a_4}{a_3}$

$r_3=\frac{8}{4}$

$r_3=2$

so,

$r_1=r_2=r_3=2$

so, this is geometric sequnce

graph-C:

we are given terms as

$a_1=2$

$a_4=4$

$a_9=6$

since, they are not in proper sequence

so, this is not geometric sequence

graph-D:

we are given terms as

$a_1=1$

$a_2=4$

$a_3=9$

now, we can find common ratios

$r_1=\frac{a_2}{a_1}$

$r_1=\frac{4}{1}$

$r_1=4$

$r_2=\frac{a_3}{a_2}$

$r_2=\frac{9}{4}$

Since, r1 is not equal to r2

so, this is not geometric sequence.........Answer