if(3-x)+(6)+(7-5x)is a geometric se ries, find two posible value for x,the common ratio and the sum of th g.p
r = 6/(3-x) OR r = (7-5x)/6
6/(3-x) = (7-5x)/6
21 - 15x - 7x + 5x^2 = 36
5x^2 - 22x - 15 = 0
(x - 5)(5x + 3) = 0
x = 5 or x = -3/5
so the common ratio could be
6/3-5) = -2
or
6/(-3/5) = -10
if r = -2, we have
-3 + 6 - 12 = -9
if r = -10 , we have
-5/3 + 6 - 60 = - 167/3
check my arithmetic
What is the common ratio
The common ratio is -3
Ratio is -3
-3,1/2/3
Why did the mathematician go to the circus? Because he heard there were some clown bots performing geometric series!
But to answer your question seriously, let's find the common ratio:
(3-x) + 6 + (7-5x)
Since these terms are in a geometric series, it means that the ratio between consecutive terms should be constant. To find this ratio, let's divide the second term by the first term, and the third term by the second term:
(6) / (3-x) = (7-5x) / 6
Now, to find possible values for x, we'll solve the equation. Brace yourself!
6(7-5x) = 6(3-x)
42 - 30x = 18 - 6x
24 = 24x
x = 1
So one possible value for x is 1.
Now let's find the common ratio. We can use any term in the series to do this. Let's use the second term:
r = (7-5x) / 6
r = (7-5(1)) / 6
r = 2/6
r = 1/3
Therefore, the common ratio is 1/3.
Now let's find the sum of the geometric series. To calculate this, we'll use the formula:
S = a / (1-r)
Where "a" is the first term and "r" is the common ratio.
Substituting the values we found:
S = (3-1) / (1 - 1/3)
S = 2 / (2/3)
S = 2 * (3/2)
S = 3
So the sum of the geometric series is 3.
Therefore, one possible value for x is 1, the common ratio is 1/3, and the sum of the series is 3.
To determine if the expression (3-x) + 6 + (7-5x) is a geometric series, we need to check if there is a common ratio between consecutive terms.
A geometric series has the form a, ar, ar^2, ar^3, ... where a is the first term and r is the common ratio.
Let's expand the expression and look for a common ratio:
(3 - x) + 6 + (7 - 5x)
Simplifying this expression, we get:
9 - 6x
Since there is only one term, we don't have consecutive terms to compare. Therefore, the expression (3-x) + 6 + (7-5x) is not a geometric series.
As there is no geometric series, we cannot find the common ratio, the sum of the geometric progression, or two possible values for x in this case.