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the first 4 terms of a 10-term geometric series are listed below. Which expression represent the sum of the series? need ASAP
16/25+8/5+4+10+...+a^10

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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