the sum of the 4th term and the 5th term is 12.if the 4th term of the progression is 8, find the common ratio and the 1st term of the progression.
Call the first term A1.
The An term is A1*r(n-1)
A4 = 8
A4 + A5 = 12 so A5 = 4 and r = 1/2 is the ratio.
Since A4 = 8, A1 = 64 is the first term
The series progression is
64, 32, 16, 8, 4, 2,...
If 10th term of a G.P. Is 9 and fourth term is 4, then its 7th term is:
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gthtrdgy3shqi27iu4t623qy35471rfgdhbhoq32utr8q4trgf31cbeuut76rd3guh
To find the common ratio and the first term of the progression, we can use the given information about the 4th and 5th terms.
Let's assume that the first term of the progression is 'a' and the common ratio is 'r'.
Since the 4th term of the progression is given as 8, we can express it as: a * r^3 = 8 ----(1)
Now, let's consider the 5th term. We are given that the sum of the 4th term and the 5th term is equal to 12. Therefore, we have: a * r^3 + a * r^4 = 12
We can substitute the value of the 4th term (8) into this equation: 8 + a * r^4 = 12
Simplifying the equation: a * r^4 = 4 ----(2)
Now, we have two equations (1 and 2) with two variables (a and r). We can solve these equations simultaneously to find the values of a and r.
First, divide equation (2) by equation (1) to eliminate 'a':
(4 / 8) = (a * r^4) / (a * r^3)
1/2 = r
So, the common ratio (r) is 1/2.
Now, substitute the value of r (1/2) into equation (1) to find 'a':
a * (1/2)^3 = 8
a * (1/8) = 8
a = 8 * 8
a = 64
Thus, the first term of the progression is 64, and the common ratio is 1/2.