The 8th term of a GP is -7/32.Find its common ratio if its first term is 28.
I don't understand please break it down
28 * r^7 = -7 / 32
4 * r^7 = -1 / 32
r^7 = -1 / 128 ... r^7 = -1 / 2^7
r = -1/2
Please break it down , the way I will understand
Know more about G.p
I don't understand please break it down
Why did the math book go to the comedy club? It wanted to find its common "ratio" of jokes!
But in all seriousness, let's solve this problem.
We know the first term (a1) is 28 and the 8th term (a8) is -7/32.
In a geometric progression (GP), the formula to find the nth term is given by:
an = a1 * r^(n-1)
So, let's plug in the known values:
a8 = 28 * r^(8-1)
-7/32 = 28 * r^7
Now let's solve for the common ratio (r):
r^7 = (-7/32) / 28
r^7 = -1/128
To simplify this equation, we can rewrite -1/128 as (-1)^1 / (2^7).
Then we get:
r^7 = (-1)^1 / (2^7)
r^7 = -1 / 128
r = (cube root of -1) / 2
So, the common ratio of the geometric progression is: (cube root of -1) / 2.
Remember, math can be a bit complex at times, but never fear, humor is here!
To find the common ratio of a geometric progression (GP), we can use the formula for the nth term of a GP:
an = a * r^(n-1)
Where:
an = nth term of the GP
a = first term of the GP
r = common ratio of the GP
n = position of the term
Given:
a = 28 (first term)
an = -7/32 (8th term)
We need to find the value of r.
Substituting the given values into the formula:
-7/32 = 28 * r^(8-1)
-7/32 = 28 * r^7
Now, let's solve for r:
Divide both sides by 28:
(-7/32) / 28 = r^7
(-7/32) * (1/28) = r^7
-7/896 = r^7
To find the 7th root of both sides, raise both sides to the power of 1/7:
(-7/896)^(1/7) = r^(7/7)
(-7/896)^(1/7) = r
Now, to evaluate the value of r, use a calculator or a math software:
r ≈ -0.4
Therefore, the common ratio of the given GP is approximately -0.4.