anonymous
  • anonymous
What is the first term of the geometric sequence presented in the table below?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1449889805991:dw|
anonymous
  • anonymous
These are the choices \[_a{1}= 4/3\]
anonymous
  • anonymous
\[_a{1}-3/4\]

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anonymous
  • anonymous
\[_a{1}=-3\]
anonymous
  • anonymous
\[_a{1}=\]
anonymous
  • anonymous
a1 = 3/4 is the last choice
mathmale
  • mathmale
Please do what you can to determine the common ratio of this geometric sequence. In other words, find the factor that multiplies each term to get the next term.
anonymous
  • anonymous
how would you begin to do that?
anonymous
  • anonymous
\[a _{n}=ar ^{n-1}\] where a is first term,r is the co mmon ratio. \[12=ar ^{3-1}=ar^2\] \[-324=ar ^{6-1}=ar^5\] divide \[\frac{ ar^5 }{ ar^2 }=\frac{ -324 }{ 12 }=-27\] \[r^3=-27=\left( -3 \right)^3,r=-3\] \[a \left( -3 \right)^2=12,a=\frac{ 12 }{ 9 }=\frac{ 4 }{ 3 }\]
anonymous
  • anonymous
thank you so much! I have another one, if you don't mind helping me
anonymous
  • anonymous
np
anonymous
  • anonymous
http://learnft.flvs.net/webdav/assessment_images/educator_lam2_v14/q144289-la_sequences_series_graph_5.jpg Using the graph above, what is the common ratio of the geometric sequence? r = 8 r = 4 r= 1/4 r = -28
anonymous
  • anonymous
sorry, iam not able to open it.
anonymous
  • anonymous
Ok its basically a graph with three integers, which are (1,32)(2,8)(3,2)
anonymous
  • anonymous
do you think you would be able to help me with that info?
mathmale
  • mathmale
(1,32)(2,8)(3,2)? It's obvious that as n increases, a sub n decreases. If n=1, \[a _{1}=32.\]
mathmale
  • mathmale
If n=2, \[a _{2}=8.\]
mathmale
  • mathmale
and so on. Again: n starts at 1 and increases by 1 each time you go to a new term, and the correspoinding a_n decreases. Big question for you: If you start with 32, by what number must you multiply it to get 8? If you start with 8, by what number must you multiply 8 to get 2?
mathmale
  • mathmale
This number is your "common ratio," which is usually symbolized by the letter "r."
mathmale
  • mathmale
In the future, would you please post no more than 1 or 2 problems at a time.
mathmale
  • mathmale
See Surjithayer's post(s) for more info on the formula for a geometric series.

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