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

80 < 93 < 121 < 127

Step-by-step explanation:

For a geometric series,

Formula to be used,

Sum of t terms of a geometric series =

Here t = number of terms

a = first term

r = common ratio

1).

   First term of this series 'a' = 3

   Common ratio 'r' = 2

   Number of terms 't' = 5

   Therefore, sum of 5 terms of the series =

                                                                      = 93

2).

   First term 'a' = 1

   Common ratio 'r' = 2

   Number of terms 't' = 7

   Sum of 7 terms of this series =

                                                    = 127

3).

    First term 'a' = 1

    Common ratio 'r' = 3

    Number of terms 't' = 5

   Therefore, sum of 5 terms =

                                                 = 121

4).

    First term 'a' = 2

    Common ratio 'r' = 3

    Number of terms 't' = 4

    Therefore, sum of 4 terms of the series =

                                                                       = 80

    80 < 93 < 121 < 127 will be the answer.