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.
