Question

Please please help i don’t understand this.

Answer 1

For a geometric sequence;
a(n) = a1*r^(n-1)

Where
a(n) = nth term
a1 = first term
r = common ratio
n = 0,1,2,3,4,5, ... n

To establish which graphs agree with this formula, each graph should be tested separately as follows:
Graph A:
a2 = 9
Then
9 = a1*(1/3)^(2-1) =1/3a1 => a1 = 3*9 = 27
Sequence:
a1 = 27
a2 = 9
a3 = 27*(1/3)^(3-1) = 3
a4 = 27*(1/3)^(4-1) = 1
These are the same values shown and thus this graph corresponds to geometric sequence.

Graph B:
a1 = 12
a2 = 12*(1/3)^(2-1) = 4
a3 = 12*(1/3)(3-1) = 4/3
a4 = 12*(1/3)^(4-1) = 4/9
These are the values shown by the graph and thus it corresponds with geometric sequence.

Graph C:
a1 = 3+3/2 = 9/2
a2 = (9/2)*(1/3)^1 = 3/2
a3 = (9/2)*(1/3)^2 = 1/2
a4 = (9/2)*(1/3)^3 = 1/6
a0 = (9/2)*(1/3)^-1 = 13.5 (this is not the case as the graph shows a0 = 12)

Therefore, this graph does not correspond to geometric sequence.

Graph D:
a1 = 4
a2 = 4*(1/3)^1 = 4/3
a3 = 4*(1/3)^2 = 4/9
a4 = 4*(1/3)^3 = 4/27
a0 = 12

This graph seems to agree with values of geometric sequence and thus corresponds to geometric sequence.

Therefore, graphs A, B, and D corresponds with geometric sequence.