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If x - 4 , x + 2 and 3x + 6 form a geometric sequence, find x.

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6 votes

Answer:

x =7

Explanation:

Remark

  • A geometric sequence always has terms that are separated by a common ratio. For example 3 9 27 81 243 ....
  • Each term is multiplied by a common number and the term before it. In this case the common term is 3.
  • To get the next term after 9, you multiply 9 by 3.
  • To get the common ratio divide the second term by the first and then the third term by the second

Equation

(x + 2)/(x - 4) = (3x + 6)/ (x + 2)

Solution

I would begin this problem by taking out the common factor on the top right term. You'll see why in a second.

(x + 2)/(x - 4) = 3(x + 2)/ (x + 2) Notice the two binomials on the right cancel.

  • (x + 2)/(x - 4) = 3/1 Cross multiply
  • (x + 2)*1 = 3*(x - 4) Remove the brackets on the right.
  • x + 2 = 3x - 12 Add 12 on both sides.
  • x + 2 + 12 = 3x - 12 + 12 Simplify
  • x + 14 = 3x Subtract x from both sides
  • 14 = 3x - x
  • 2x = 14 Divide by 2
  • x = 14/2
  • x = 7
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