anonymous
  • anonymous
If 16, x, 9 are the first 3 terms of a geometric sequence, find the exact value of x can someone tell me how to find it please :) thanks
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[{16 \over x}={x \over 9}\]
anonymous
  • anonymous
\(x=12\)
anonymous
  • anonymous
\(x=-12\) is also a solution.

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anonymous
  • anonymous
16=4^2 9=3^2 x should be 3.5^2 = 12.25
anonymous
  • anonymous
A geometric sequence is a sequence in which a term \(a_i\) can be found by multiplying the previous term \(a_{i-1}\) by some constant \(d\). In our case d could be \(-3/4\) or \(3/4\).
anonymous
  • anonymous
??? i got 3/4 too but thats wrong the right answer is 12 but i dont understand how they got it why did you put it in a fraction???
anonymous
  • anonymous
Yeah x is either \(12\) or \(-12\). You get it by solving the equation I put in my first comment.
anonymous
  • anonymous
In a geometric sequence, the quotient of any two consecutive in the sequence must give the same value. So, in our case, \(16/x =x/9\). Solve this equation for x and you will get the answer.
anonymous
  • anonymous
thank you :)
anonymous
  • anonymous
You're welcome :)

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