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Sagot :
Using geometric sequence concepts, it is found that the sum of the first 10 terms is of 4068.6.
What is a geometric sequence?
- A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
- In which [tex]a_1[/tex] is the first term.
The sum of the first n terms is given by:
[tex]S_n = \frac{a_1(q^n-1)}{q - 1}[/tex]
In this problem, the sequence is:
[tex]\frac{16}{25}, \frac{8}{5}, 4, 10,...[/tex]
Hence:
[tex]a_1 = \frac{16}{25}, q = \frac{10}{4} = 2.5[/tex]
Then, the sum of the first 10 terms is:
[tex]S_{10} = \frac{\frac{16}{25}(2.5^{10}-1)}{2.5 - 1} = 4068.6[/tex]
You can learn more about geometric sequence concepts at https://brainly.com/question/11847927
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