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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