Question 118821: In the geometric sequence the first three terms are ( 5x-8,3x,2x+2,...).What is the value of x ? Please help me :)
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Find the value of x if the first three terms of a geometric sequence are given as:
{5x-8, 3x, 2x+2,...}
You know that in a geometric sequence, consecutive terms have a common ratio.
This can be expressed as:
 or, in words...Any term divided by the previous term is a constant called the common ratio, r.
So, let's use this useful fact to find x in your problem:
 and...
 and, since k = k, we can set these two equal to each other:
 Simplify and solve for x.
 Expand.
 Subtract  from both sides.
 Solve this quadratic equation by factoring.
 Apply the zero product principle:
 or 
If then  or
if then 
So there are two possible solutions for x.
or and since the problem does not give us the common ratio, both values of x are valid solutions.
Check:
{5x-8, 3x, 2x+2,...} Let's try x = -2
{5(-2)-8, 3(-2), 2(-2)+2,...}
{-18, -6, -2,...} The common ratio, r, is:
 OK
Now try x = 8:
{5x-8, 3x, 2x+2,...}
{5(8)-8, 3(8), 2(8)+2,...}
{32, 24, 18,...} The common ratio here is:
 OK
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