Question

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

Answer 1

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.

Answer 2

D. 2 + 14 + 98 + 686

Explanation:

A. 6 + 13 + 20 + 27 .

the difference between two terms are 13-6 = 7 , 20-13= 7

The terms are increasing by 7. So it is not geometric

B. 7 + 21 + 35 + 45

the difference between two terms are 21-6 = 14 , 35-21= 14

The terms are increasing by 14. So it is not geometric

C. 14 + 21 + 28 + 35

the difference between two terms are 21-14 = 7 , 28-21= 7

The terms are increasing by 7. So it is not geometric

D. 2 + 14 + 98 + 686

Here the difference is not same, so we find the ratio

14/2= 7

98/14= 7

686/98= 7

So common ratio is 7

When the common ratio is same then it is Geometric series