The first and the third term of a GP are 5 and 80 respectively.what is the fourth term.
5 r^2 = 80 ... r^2 = 16
To find the fourth term of a geometric progression (GP), you need to know the values of the first term (a) and the common ratio (r).
In this case, the first term (a) is given as 5, and the third term is given as 80.
We can use this information to find the common ratio (r). The formula to find the n-th term of a GP is:
an = a * r^(n-1)
For the third term, we substitute n = 3 and a = 5:
80 = 5 * r^(3-1)
80 = 5 * r^2
Divide both sides by 5:
16 = r^2
Taking the square root of both sides gives us:
r = ±√(16) = ±4
So, the common ratio can be either 4 or -4.
Now, we can find the fourth term by substituting n = 4 and a = 5 into the formula:
a4 = a * r^(4-1)
For r = 4:
a4 = 5 * 4^(4-1)
a4 = 5 * 4^3
a4 = 5 * 64
a4 = 320
For r = -4:
a4 = 5 * (-4)^(4-1)
a4 = 5 * (-4)^3
a4 = 5 * (-64)
a4 = -320
Therefore, the fourth term can be either 320 or -320, depending on the sign of the common ratio.