Question

The geometric sequence an = 1/5an-1 with an initial value of a1 = 125 represents the sales of a specific

Answer 1

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:

$a_n = a_1*r^{n-1}$

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

$S_N = a_1*(r^N - 1)/(r - 1)$

Here we know that:

$a_n = (1/5)*a_{n-1}$

So the common ratio is r = 1/5

And we also know that:

$a_1 = 125$

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

$S_8 = 125*( (1/5)^8 - 1)/( 1/5 - 1) = 156.25$

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

brainly.com/question/9300199