Arrange the geometric series from least to greatest based on the value of their sums.

Step-by-step explanation:

A geometric sequence is a sequence in which the next term is gotten from the previous term by multiplication by a constant. The series is an addition of the terms in the sequence.

E.g (i) 2,4,8,16… (ii)9,3, 1/3, 1/9,…

In example (I) the constant is 2 while in example (ii) the constant is 1/3.

This constant is referred to as the common ratio r.

To add the terms in a Geometric Series, if the common ratio r is greater than 1, we use

And if it is less than 1

Where a= the first term, n= number of term to be added and r= the common ratio.

This can be applied to any given geometric series to arrange it in ascending or descending order by its sum.

37

step-by-step explanation: