6x+12,2x+4 and x-7 are the first three terms of a geometric sequence.

Question

-is this a converging or diverging sequence...justify your answer

Answer 1

If there is a common ratio, then you need

(2x+4)/(6x+12) = (x-7)/(2x+4)
x = 25

So, the common ratio is 54/162 = 1/3

Since |r| < 1, the sequence converges.