IN A GP THE 5TH AND 8TH IS 24 AND 72 FIND THE 6TH
what is half of 4
To find the 6th term in a geometric progression (GP), we need to determine the common ratio (r) first. The common ratio is found by dividing any term in the GP by its preceding term.
In this case, we can find the common ratio by dividing the 8th term (72) by the 5th term (24):
r = 72 / 24
Next, we evaluate r:
r = 3
Now that we know the common ratio, we can find the 6th term. To do this, we multiply the 5th term (24) by the common ratio (3):
6th term = 24 * 3
Simplifying the equation gives us:
6th term = 72
To find the 6th term of the geometric progression (GP), we first need to determine the common ratio (r) of the progression.
In a geometric progression, each term is found by multiplying the previous term by a constant ratio (r). Mathematically, the formula to find the nth term (a_n) in a geometric progression is: a_n = a * r^(n-1), where "a" is the first term.
Given that the 5th term (a_5) is 24, and the 8th term (a_8) is 72, we can set up two equations to find the common ratio (r).
1. For the 5th term:
a_5 = a * r^(5-1) = 24
2. For the 8th term:
a_8 = a * r^(8-1) = 72
To solve these equations, we can divide the second equation by the first equation to eliminate the "a":
(a * r^7) / (a * r^4) = 72 / 24
Simplifying,
r^3 = 3
Taking the cube root of both sides,
r = ∛3
Now that we have the value of the common ratio (r), we can find the 6th term (a_6) using the first equation:
a_6 = a * r^(6-1)
Substituting the known values:
a_6 = a * (∛3)^5
The value of the 6th term will depend on the value of the first term (a) in the geometric progression. If you provide the first term, I can calculate the 6th term for you.