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iris [78.8K]
2 years ago
11

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

Mathematics
1 answer:
lesya692 [45]2 years ago
3 0

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

<h3>Sum of the first N terms in a geometric sequence.</h3>

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

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Answer:

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Step-by-step explanation:

Given

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According to SOH CAH TOA

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Get the adjacent using the pythagoras theorem

hyp² = opp²+adj²

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adj = √-55

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Get cosjk

cosjk = adj/hyp

cosjk = √55 i/3

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