contestada

The geometric sequence an = 1/5an-1 with an initial value of a1 = 125 represents the sales of a specific
product at a store, where n is the number of years after its release. What is the sum of the first 8 terms?

Respuesta :

facundo3141592

Here we want to get the sum of the first 8 terms for the given geometric sequence, we will find that the solution is: 156.25

Sum of the first N terms in a geometric sequence.

We know that for a geometric sequence given by:

[tex]a_n = a_1*r^{n-1}[/tex]

Where r is the common ratio, the sum of the first N terms is given by:

[tex]S_N = a_1*(r^N - 1)/(r - 1)[/tex]

Here we know that:

[tex]a_n = (1/5)*a_{n-1}[/tex]

So the common ratio is r = 1/5

And we also know that:

[tex]a_1 = 125[/tex]

Then we can replace these two in the formula for the sum with N = 8 to get:

[tex]S_8 = 125*( (1/5)^8 - 1)/( 1/5 - 1) = 156.25[/tex]

If you want to learn more about geometric sequences, you can read:

https://brainly.com/question/9300199

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