To find the sum of the first four terms of a geometric progression (GP), we need to determine the common ratio (r) and the first term (a).
Given that the 2nd term is -6 and the 5th term is 48, we can set up the following equations:
a * r = -6 —(1) a * r^4 = 48 —(2)
Dividing equation (2) by equation (1), we get:
(r^4)/(r) = 48/(-6) r^3 = -8
Taking the cube root of both sides, we find:
r = -2
Substituting the value of r into equation (1), we can solve for a:
a * (-2) = -6 a = -6 / (-2) a = 3
Now that we have the common ratio (r = -2) and the first term (a = 3), we can calculate the sum of the first four terms using the formula:
Sum of first n terms = a * (1 – r^n) / (1 – r)
For n = 4, we have:
Sum = 3 * (1 – (-2)^4) / (1 – (-2)) = 3 * (1 – 16) / (1 + 2) = 3 * (-15) / 3 = -15
Therefore, the sum of the first four terms of the geometric progression is -15.