The third and fourth of a geometric progression are 4 and 8 respectively. Find the first and the common
clearly, r = 8/4 = 2
so, ar^2=4
a=1
The sequence is 1,2,4,8,16,...
To find the first term and the common ratio of a geometric progression, you can use the given information about the third and fourth terms.
Let's denote the first term as 'a' and the common ratio as 'r'.
Given:
The third term = 4
The fourth term = 8
We know that the nth term of a geometric progression is given by the formula:
an = a * r^(n-1)
Using this formula, we can set up two equations using the given information:
Equation 1: a * r^2 = 4 (since the third term is 4)
Equation 2: a * r^3 = 8 (since the fourth term is 8)
Now, we can solve these equations to find the values of 'a' and 'r'.
Dividing Equation 2 by Equation 1:
(a * r^3) / (a * r^2) = 8 / 4
r^3 / r^2 = 2
r^(3-2) = 2
r = 2
Now that we know the common ratio 'r' is 2, we can substitute it back into Equation 1 to find the first term 'a':
a * (2^2) = 4
4a = 4
a = 1
Therefore, the first term is 1 and the common ratio is 2.