Question 1136334: If x-4,x+2 and 3x+6 form a geometric sequence, find x.
Found 3 solutions by rothauserc, MathLover1, greenestamps:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! I assume that x-4, x+2, 3x+6 are the first three terms of the geometric sequence
:
The general form of the nth term of a geometric sequence is
:
x(n) = ar^(n-1)
:
x(1) = a = x-4
:
x(2) = (x-4) * r = x+2
:
x(3) = (x-4) * r^2 = 3x+6
:
therefore, we have two equations in two unknowns
:
1) (x-4) * r = x+2
:
2) (x-4) * r^2 = 3x+6
:
solve equation 1 for r
:
r = (x+2)/(x-4)
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substitute for r in equation 2
:
(x-4) * (x+2)/(x-4) * (x+2)/(x-4) = 3(x+2)
:
simplify the result by canceling an (x-4) from numerator and denominator, also cancel (x+2) from both sides of equal sign
:
(x+2)/(x-4) = 3
:
x+2 = 3x-12
:
2x = 14
:
x = 7
:
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x = 7
:
geometric sequence is 3, 9, 27 and common ratio is 3
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Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! If  , and  form a geometric sequence, find  .
A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio,  .
given:
find ratio using given terms:
plug it in  using third term
 ....simplify
 .....cross multiply
 ....simplify
 ......factor
solutions:
 or 
so, your terms are:
if
 , ,  ->In this example we have  and 
so, nth term formula is:
 ....apply exponents product rule
or
if
 , , ->the sequence is neither arithmetic or geometric; so, disregard
your answer is: 
Answer by greenestamps(13209)  (Show Source):
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