anonymous
  • anonymous
Write an expression for the general or nth term, an, for the geometric sequence. 1, -4, 16, -64... A. An=1.(-4)^n-1 B. An=1.(-4)^n C. An=1.4^n-1 D. An=1.4^n
Mathematics
schrodinger
  • schrodinger
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freckles
  • freckles
so have you notice the common ratio for example what are the following equal to: \[\frac{-4}{1}=? \\ \frac{16}{-4}=? \\ \frac{-64}{16}=?\] notice I just did term/previous term
anonymous
  • anonymous
Is it 4?
freckles
  • freckles
you should find that those all equal to -4 which they should have term/previous term hold a constant number since they claimed it was a geometric sequence but anyways since the common ratio is -4 you can definitely rule out C and D and only look at A and B

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freckles
  • freckles
Now the only way I can answer if it is A or B is if you tell me if your class uses n=0 for the first term or you use n=1 for the first term
freckles
  • freckles
I bet it is n=1
freckles
  • freckles
but if you know this will really be needed because both of those could described the sequence depending on how n is defined
freckles
  • freckles
anyways if it is n=1 which of the following gives 1 as the answer: \[A_1=1(-4)^{1-1} \text{ using choice A here } \\ A_1=1(-4)^{1} \text{ using choice B here }\]
freckles
  • freckles
we are looking to see which gives A_1 as 1 since 1 is the first number in the sequence
anonymous
  • anonymous
Okay, thanks. I think it's A.
freckles
  • freckles
yes that is only if your class uses n=1 to give first term

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