SOLUTION: Consider a sequence 4, x, 9, ... with x>0 If the sequence is geometic, find (a) the value of x, (b) the value of t<sub> 6</sub>, (c) a formula for t<sub> n</sub> and (d) the value

Algebra ->  Sequences-and-series -> SOLUTION: Consider a sequence 4, x, 9, ... with x>0 If the sequence is geometic, find (a) the value of x, (b) the value of t<sub> 6</sub>, (c) a formula for t<sub> n</sub> and (d) the value      Log On


   

Question 82382This question is from textbook
: Consider a sequence 4, x, 9, ... with x>0
If the sequence is geometic, find (a) the value of x, (b) the value of t 6, (c) a formula for t n and (d) the value of S 6 This question is from textbook

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Consider a sequence 4, x, 9, ... with x>0
If the sequence is geometic, find (a) the value of x, (b) the value of t 6, (c) a formula for t n and (d) the value of S 6
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r=x/4=9/x
Therefore x^2=36 and x=6.
Therefore r=6/4=3/2
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t(6) = [t(1)]
t(6) = 4*(3/2)^5 = 30.375
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t(n) = [t(1)][r^(n-1)]
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S(n) = [r^(n+1)-1]/[r-1]
S(6) = [(3/2)^7-1]/[(3/2)-1]
S(6) = [16.0859...]/[0.5]=32.172
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Cheers,
Stan H.