Write a formula for the general term (the nth term) of the geometric sequence. 1/2 -1/10 1/50 -1/250

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Write a formula for the general term (the nth term) of the geometric sequence. 1/2 -1/10 1/50 -1/250

Mathematics
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A. an = 1/2(n-1)3/5 B. an = 1/2 - 1/5(n-1) C. an = (1/2)(-1/5)(n-1) D. an = (1/5)(-1/2)(n-1)
  • phi
any idea how to "get" from 1/2 to -1/10 ? what do you multiply 1/2 by to get -1/10 ?

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Other answers:

5 maybe
  • phi
right track. but you can do better \[ \frac{1}{2} \cdot x =- \frac{1}{10} \]
  • phi
if you multiply by 5 you get \[ \frac{5}{2} \] not what we want
1/5
  • phi
if you can't see it, try multiplying both sides by 2 and "solve for x" 1/5 is pretty good, but not quite \[ \frac{1}{2} \cdot \frac{1}{5}= \frac{1}{10} \] but we want \[ - \frac{1}{10} \]
so -1/5
  • phi
ok, and to make sure take the 2nd term in the series -1/10 and multiply by -1/5 what do we get ?
1/15
i think
  • phi
multiply top times top and bottom times bottom
ok so 1/50
  • phi
and if we multiply 1/50 by -1/5 we get -1/250 notice we are getting the original series 1/2 -1/10 1/50 -1/250
yes
  • phi
here is what we know \[ \frac{1}{2} \\ \frac{1}{2}\left(-\frac{1}{5}\right)^1 \\ \frac{1}{2}\left(-\frac{1}{5}\right)^2 \] and so on
yes
  • phi
if we label the first term as "term number 1" and the 2nd 2 and then 3 etc notice each term has 1/2 times (-1/5) to a power one less than the term's number
yes that makes sence
  • phi
only one of the choices is "short-hand" for that
c
  • phi
yes
yeah thnx again freind

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