The 2nd and 5th terms of a Gp are -5 and 48 respectively.find the sum of the first four terms.

in a GP

term(2) = ar = -5
term(5) = ar^3 = 48

ar^3/(ar) = -48/5
r^2 = -9.6
no real solution possible

21340

the 2nd 5th term of an g p are -6 and 48 vespectively find the sum of the frist four terms N A E C

To find the sum of the first four terms of a geometric progression (GP), we need to determine the common ratio (r) first.

Given that the 2nd term is -5 and the 5th term is 48, we can set up the following equations:

a * r = -5 ---(1)
a * r^4 = 48 ---(2)

By dividing equation (2) by equation (1), we can eliminate "a" and solve for "r":

(a * r^4) / (a * r) = 48 / (-5)
r^3 = -48/5

Now, taking the cube root of both sides, we get:

r = (∛(-48/5))

Simplifying this value of "r" gives us the common ratio:

r = -2/∛5

Once we have the common ratio, we can use the formula for the sum of the first "n" terms in a GP:

Sum = a * (1 - r^n) / (1 - r)

In this case, we want to find the sum of the first four terms (n = 4):

Sum = a * (1 - (-2/∛5)^4) / (1 - (-2/∛5))

Now, substitute the known values into the formula to calculate the sum.