anonymous
  • anonymous
What is the sum of the geometric sequence 1, 4, 16, ... if there are 8 terms?
Mathematics
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SOLVED
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chestercat
  • chestercat
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tkhunny
  • tkhunny
1 + 4 + 16 + ... + 4^(n-1) + ... + 4^(7) Are you SURE you can't add those up? Personally, I'd do it this way: \(\dfrac{1 - 4^{8}}{1-4}\). You may have another formula based on a, r, and n.
anonymous
  • anonymous
I can add :) I just am mostly unsure of the equation to use. But YES! The equation I'm supposed to use involves a, r, and n!
tkhunny
  • tkhunny
Okay, then what is preventing you from using it? a = 1 r = 4 n = 8 Go!

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anonymous
  • anonymous
Funny story: I do online classes and I am usually very good at following formulas. Although for whatever reason the review equations that I applied to my previous homework made me get EVERYTHING wrong! So now I have no idea which kind of equations to use, on which kind of geometric series or sequences or arithmetic sequences or series
tkhunny
  • tkhunny
Sad, sad, how many of these online courses just don't seem to be doing the job they claim to be doing! Arithmetic Sequence Each successive term differs from its predecessor by a constant. Example: 1, 2, 3, 4, 5, ... Each term is one (1) great than the previous. Geometric Sequence Each successive term differs from its predecessor by a ratio. Example: 1, 2, 4, 8, 16, ... Each term is twice the previous. Okay, what sort of Series have you?
anonymous
  • anonymous
I'm actually one the very end of my course and sudden;y everything that i'm learning is wrong :( the one I just posted would be a geometric sequence, right?
anonymous
  • anonymous
yes it is a geometric sequence with r=4 meaning that every next number is multiplied by four: \[\sum_{n=1}^{8}4n\]so literally you're just adding it up \(1+4+16+64+256+1,024+4,096+16,384=21,845\)

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