The geometric series will be D. 2 + 14 + 98 + 686 because it is having a common ratio 7.
What is geometric series?
In mathematics, a geometric series is the sum of an infinite number of terms that have a constant or common ratio between successive terms
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
Hence the geometric series will be D. 2 + 14 + 98 + 686 because it is having a common ratio 7.
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