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.