anonymous
  • anonymous
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768, respectively.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
i understand how to do this when the two terms are already consecutive, but im not sure where to start with this one
Jhannybean
  • Jhannybean
what is the ratio?
anonymous
  • anonymous
how do i find the ratio without two consecutive terms?

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More answers

Jhannybean
  • Jhannybean
Grr...
anonymous
  • anonymous
:x sorrry
anonymous
  • anonymous
im not just looking for an answer, i legitimately want help understanding how to work the problem, i just need help through most of it
Jhannybean
  • Jhannybean
Yeah..i'm trying to work it out to explain it to you,but having difficulty finding the ratio.
radar
  • radar
Would knowing the ratio r be helpful?
jim_thompson5910
  • jim_thompson5910
a2 = -12 a3 = a2*r = -12r a4 = a3*r = (-12r)*r = -12r^2 a5 = a4*r = (-12r^2)*r = -12r^3
jim_thompson5910
  • jim_thompson5910
because a5 = 768, we can say 768 = -12r^3
radar
  • radar
There you go, now you can solve for r
Jhannybean
  • Jhannybean
nice!
anonymous
  • anonymous
so, 768/-12 = r^3 -64 = r^3 -4 = r
anonymous
  • anonymous
an = a1(-4)^n-1
anonymous
  • anonymous
im sorry, but now now how would i find the first term to use in the rule?
Loser66
  • Loser66
show me how you have the form above? an? one more question, does your prof ask you have to prove what you claim before using it to find our the nth term?
Loser66
  • Loser66
*out
anonymous
  • anonymous
a subscript n
jim_thompson5910
  • jim_thompson5910
Use the idea Second term = (First term)*r
anonymous
  • anonymous
nth term = (first term)(ratio)^n-1
anonymous
  • anonymous
that was the basis of my lesson. im virtual schooled, so the lessons are very impersonal, leaving much to the student to figure out on their own
Jhannybean
  • Jhannybean
\[\large a_{2} =?\]\[\large r=?\]\[\large a_{1}=?\] plug into equation \[\large a_{2}=a_{1}*r\]
Loser66
  • Loser66
or a1 = a2/r
anonymous
  • anonymous
would it be an = 3(-4)^n-1
Jhannybean
  • Jhannybean
yep
anonymous
  • anonymous
okay, thank you all

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