SOLUTION: The sum of a finite geometric sequence for n terms with common ratio r and initial term a1 is: s(n)=a1 (1-r^n/1-r) Find the sum of the first 10 terms of 4, 2, 1, 1/2, 1/4

Question 422414: The sum of a finite geometric sequence for n terms with common ratio r and initial term a1 is:
s(n)=a1 (1-r^n/1-r)
Find the sum of the first 10 terms of 4, 2, 1, 1/2, 1/4
I am EXTREMELY stuck and don't know where to even begin! All help is greatly appreciated! thanks!
Found 3 solutions by solver91311, ewatrrr, richard1234:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

First, please satisfy my curiosity. How does being EXTREMELY stuck compare to being quite stuck, or very stuck, or extraordinarily stuck, or even just plain stuck? Is being EXTREMELY stuck different than being Extremely stuck or extremely stuck? If so, by how much or what factor do they differ? Do you think that the relative degree to which you are stuck should have a bearing on the amount of help you get or the rapidity with which it is provided?

I'll give you some help with that last question. The answer is unequivocally no. I'll also give you some pointers on how to improve your chances of a quick, detailed, and accurate response.

1. Don't start with an untruth. You posted the formula, hence your claim that you "don't know where to even [sic] begin" is a patently false statement on its face. I suspect you are clever enough to determine the first number in the series, , and the number of numbers in the series, , because both of these values were given.

2. Show the work you have done so far, or at least ask a question that shows that you have given the question some independent thought. Perhaps the idea of a common ratio is giving you trouble, so a statement like "I don't know how to determine the common ratio" would have gotten an immediate answer.

3. Review your post before submitting it. If it sounds more like you are whining and begging than a scholarly discussion of a mathematics concept, then revise before sending.

John

My calculator said it, I believe it, that settles it

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi
Geometric sequence {4,2,1,1/2,1/4...}
what is the relationship between one term to the next?? r = 1/2
a1 = 4

= 4*(1-.5^10)/.5 = 8*.999 = 7.992
Note: with r <|1| Sum = a1/(1-r) = 4/.5 = 8 approximates the sum!
The sum of an infinite number of terms of this sequence = 8
(1/2)^20 = .00000095 for example,
demonstrates what happens to value of (1-r^20) as n gets large
Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
I agree with the other tutor. You have , because the ratio between successive terms is 1/2, and because there are ten terms. Now it's just replacing numbers into a formula; it shouldn't get you extremely (or EXTREMELY) stuck.
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