The 8th term of a g.p is -7/32 fine it's common ration if its first term is 28
term 1 = a = 28
term 2 = a r
term 3 = a r^2
term 8 = a r^7 = -7/32
28 r^7 = -7/32
r^7 = -1/(4*32)
r^7 = -1/2^7
r = -1/2
DAT NOT THE EXAMPLE GIVEN TO US THE FORMULAR IS DIFFERENT
To find the common ratio (r) of a geometric progression (G.P.), we can use the formula for the nth term of a G.P.:
an = a * r^(n-1)
Given:
a = 28 (first term)
an = -7/32 (8th term)
n = 8
Let's substitute these values into the formula and solve for r:
-7/32 = 28 * r^(8-1)
-7/32 = 28 * r^7
Next, let's simplify the equation by dividing both sides by 28:
(-7/32) / 28 = r^7
-7/896 = r^7
To solve for r, we can take the seventh root of both sides:
r = ∛(-7/896)
Therefore, the common ratio (r) of the geometric progression is -1/4.
To find the common ratio of a geometric progression (g.p.), we need to use the formula:
an = a1 * r^(n-1)
where 'an' represents the nth term of the g.p., 'a1' is the first term, 'r' is the common ratio, and 'n' is the position of the term in the progression.
In this case, we are given the following values:
- 8th term (an) = -7/32
- First term (a1) = 28
- Position of the term (n) = 8
We can substitute these values into the formula and solve for the common ratio (r):
-7/32 = 28 * r^(8-1)
Now, let's simplify the equation by dividing both sides by 28 and multiplying by 32 to remove the fraction:
-7/32 * 32/28 = r^7
This simplifies to:
-1/4 = r^7
To find the common ratio 'r', we can take the seventh root of both sides of the equation:
r = ∛(-1/4)
The seventh root (∛) can be found using a calculator or by raising -1/4 to the power of 1/7:
r ≈ -0.5
Therefore, the common ratio of the geometric progression is approximately -0.5.