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3 years ago

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

Mathematics

2 answers:

Westkost [7]3 years ago

8 0

Answer:

Found the answer

Step-by-step explanation:

And as always have a fantastic day :)

son4ous [18]3 years ago

4 0

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.

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