anonymous
  • anonymous
What are the explicit equation and domain for a geometric sequence with the first term of 5 and a second term of -10?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
an=5(-2)^(n-1); all integers when n≥1 an=5(-2)^(n-1); all integers where n≥0 an=5(-15)^(n-1); all integers where n≥1 an=5(-15)^(n-1); all integers where n≥0
anonymous
  • anonymous
anonymous
  • anonymous

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anonymous
  • anonymous
anonymous
  • anonymous
yay @phi is here
anonymous
  • anonymous
I'm pretty sure the second half is n≥1
anonymous
  • anonymous
right?
phi
  • phi
You could test each choice. You should get 5, -10 as the first two numbers.
anonymous
  • anonymous
a
anonymous
  • anonymous
wait
anonymous
  • anonymous
b
anonymous
  • anonymous
no a
anonymous
  • anonymous
omg im so confused
phi
  • phi
***an=5(-2)^(n-1); all integers when n≥1*** for n=1 you get \[ a_1 = 5(-2)^{1-1} \\ a_1 = 5\cdot (-2)^0 \] anything to the zero power is 1 , so that simplifies to \[ a_1= 5 \cdot 1 \\a_1=5\] that looks good so far
phi
  • phi
now find a2 for choice A, using n=2
anonymous
  • anonymous
a2=5(-2)^(2-1) =5(-2)^1 =-10
phi
  • phi
yes. so choice A looks like the answer. You could double check the other three, but they won't work (give 5, -10)
anonymous
  • anonymous
ok thank you i have another but i don't know how to post the graphs so oh well
phi
  • phi
do you know how to take a screen shot?
anonymous
  • anonymous
the wording is horrible
anonymous
  • anonymous
yeah put its on my other computer hang on
anonymous
  • anonymous
It says which logarithmic graph can be used to approximate the value of y in the equation 2^y=3
anonymous
  • anonymous
i don't know how to log that?
phi
  • phi
take the log of both sides. Log base 2 is the most convenient, but log base 10 or log base 3 (natural log) all can be used. use the "rule" \[ \log(a^b) = b \log(a) \]
anonymous
  • anonymous
so… log10 2^y= log10 3
phi
  • phi
and then use the rule to write \[ y \log 2 = \log 3 \\ y = \frac{\log 3}{\log 2} \]
phi
  • phi
to get the answer from a graph, we need to figure out what log base they used. for example, what is the x value that corresponds to y=1 (that should give us the base)
phi
  • phi
Here are 3 possible logs if they gave you log base 2, read off the y value at x=3
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anonymous
  • anonymous
thank you i got it

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