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

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