Question

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

Answer 1

Answer:

Found the answer

Step-by-step explanation:

And as always have a fantastic day :)

Answer 2

Answer:

80 < 93 < 121 < 127

Step-by-step explanation:

For a geometric series,

$\sum_{t=1}^{n}a(r)^{t-1}$

Formula to be used,

Sum of t terms of a geometric series = $\frac{a(r^t-1)}{r-1}$

Here t = number of terms

a = first term

r = common ratio

1). $\sum_{t=1}^{5}3(2)^{t-1}$

   First term of this series 'a' = 3

   Common ratio 'r' = 2

   Number of terms 't' = 5

   Therefore, sum of 5 terms of the series = $\frac{3(2^5-1)}{(2-1)}$

                                                                      = 93

2). $\sum_{t=1}^{7}(2)^{t-1}$

   First term 'a' = 1

   Common ratio 'r' = 2

   Number of terms 't' = 7

   Sum of 7 terms of this series = $\frac{1(2^7-1)}{(2-1)}$

                                                    = 127

3). $\sum_{t=1}^{5}(3)^{t-1}$

    First term 'a' = 1

    Common ratio 'r' = 3

    Number of terms 't' = 5

   Therefore, sum of 5 terms = $\frac{1(3^5-1)}{3-1}$

                                                 = 121

4). $\sum_{t=1}^{4}2(3)^{t-1}$

    First term 'a' = 2

    Common ratio 'r' = 3

    Number of terms 't' = 4

    Therefore, sum of 4 terms of the series = $\frac{2(3^4-1)}{3-1}$

                                                                       = 80

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