Which of the following is a geometric series? a. 6 + 13 + 20 + 27 b. 7 + 21 + 35 + 45 c. 14 + 21 + 28 + 35 d. 2 + 14 + 98 + 686

You should not be using " + " between the series values.  You're indicating addition:  the sum of 6, 13, 20 and 27.  That's not what's intended here.

{6, 13, 20, 27} represents four terms of an arithmetic series.  Notice that from 6 we get 13 by adding 7 to 6; from 13 we get 20 by adding 7 to 13, and so on.  This is not a geom. series.

Likewise, B is an arith. series.

Likewise, C is an arith. series.

Look at the four given members of D:  {2, 14, 98, 686} (this is set notation):

14 is obtained not through addition, but rather through mult. 2 by 7.  Likewise, 98 is 7 times 14 and 686 is 7 times 98.  This is a geom. series.