If 6th term of a GP is 9375 and its 4th term is 375.find its 9th term?
geometric, not arithmetic
A6 = ar^5 = 9375
A4 = ar^3 = 375
A6/A4 = r^2 = 9375/375 = 25
r = ±5
A9 = A6*r^3 = 9375 * ±125 = ±1171875
To find the 9th term of a geometric progression (GP) given its 6th and 4th terms, we need to determine the common ratio (r) first.
Let's label the 4th term as a₁ and the 6th term as a₂. We know that a₂/a₁ = r.
From the given information:
a₁ = 375
a₂ = 9375
Using the formula a₂/a₁ = r, we can substitute the values:
9375/375 = r
Simplifying this equation gives:
r = 25
Now that we have the common ratio (r = 25), we can find the 9th term (a₉) using the formula aₙ = a₁ * r^(n-1), where a₁ is the first term (375) and n is the term number (9).
Substituting the values into the formula, we get:
a₉ = 375 * 25^(9-1)
Simplifying this expression gives:
a₉ = 375 * 25^8
Calculating this value would give you the 9th term of the GP.
To find the 9th term of a geometric progression (GP) given the 6th term and the 4th term, we need to determine the common ratio (r) of the GP first. Once we have the common ratio, we can use it to find the 9th term.
Let's use the given information to find the common ratio:
The 4th term of the GP is 375, and the 6th term is 9375.
We can set up the following equation to find the common ratio (r):
4th term = a * r^3
6th term = a * r^5
where 'a' is the first term of the GP.
Substituting the given values:
375 = a * r^3 ---(Equation 1)
9375 = a * r^5 ---(Equation 2)
Now, divide Equation 2 by Equation 1 to eliminate 'a':
9375/375 = (a * r^5)/(a * r^3)
25 = r^2
Take the square root of both sides to solve for 'r':
√25 = √(r^2)
5 = r
Now that we have found the common ratio r = 5, we can find the 9th term of the GP:
To find the 9th term, we can use the formula:
9th term = a * r^8
Substituting the value of 'r' we found earlier:
9th term = a * (5^8)
9th term = a * 390625
Since we do not have information about the first term (a), we cannot determine the exact value of the 9th term without that information.
a+5d=9375....(1)
a+4d=375....(2)
find a&d wont be difficult now just subtract 1 from 2
t9=a+8d