Arithmetic Sequence

Question

Let
X-2, X, X+3
Be the first 3 terms of a geometric sequence. Find the value of X…

Answer 1

In a geometric sequence you have a common ratio between any two consecutive terms.  Therefore x/(x - 2) = (x + 3)/x.

 

solving for x:  x/(x - 2) = (x +3)/x

                    x² = (x - 2)(x + 3)

                    x² = x² - 2x + 3x - 6

                    x² = x² + x - 6

         subtracting x² from both sides yields 0 = x - 6, therefor x = 6.

 

The terms in the sequence are x - 2 = 4

                                                x = 6

                                           x + 3 = 9

 

The check is 9/6 = 6/4, the common ratio is 3/2.