The 3rd and 4th term of a geometric progression are 4 and 8 respectively fine the frist term and common ration
To find the first term and the common ratio of a geometric progression, we can use the following formula:
an = a1 * r^(n-1)
where:
- an is the nth term of the geometric progression,
- a1 is the first term of the geometric progression,
- r is the common ratio of the geometric progression.
Given that the 3rd term is 4 and the 4th term is 8, we can substitute these values into the formula:
a3 = a1 * r^(3-1) = 4
a4 = a1 * r^(4-1) = 8
Now we have a system of two equations with two unknowns:
a1 * r^2 = 4 ---(1)
a1 * r^3 = 8 ---(2)
To solve this system, we can divide equation (2) by equation (1), which gives:
(r^3) / (r^2) = 8 / 4
Simplifying, we get:
r = 2
Now, substituting this value of r into equation (1), we can solve for a1:
a1 * (2^2) = 4
a1 * 4 = 4
Dividing both sides by 4, we get:
a1 = 1
Therefore, the first term (a1) is 1 and the common ratio (r) is 2.