Question

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

Answer 1

Answer:

x =7

Step-by-step 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