If the 2nd and 5th term of a geometric progression are -6 and 48 respectively. Find the sum of the first four terms.
Use your formulas
ar = -6
ar^4 = 48
divide them:
r^3 = -8
r = -2
now find a, then use the formula for the sum(n) terms
let me know what you get, so I can check it
To find the sum of the first four terms of a geometric progression, we need to know the first term and the common ratio.
Let's denote the first term as 'a' and the common ratio as 'r'.
We are given that the 2nd term is -6, so we can write:
a * r = -6 ---- (1)
We are also given that the 5th term is 48, so we can write:
a * r^4 = 48 ---- (2)
Now we can solve these two equations simultaneously to find the values of 'a' and 'r'.
Divide equation (2) by equation (1):
(a * r^4) / (a * r) = 48 / -6
r^3 = -8
Taking the cube root, we get:
r = -2
Now substitute the value of 'r' into equation (1):
a * (-2) = -6
a = -6 / -2 = 3
Therefore, the first term 'a' is 3 and the common ratio 'r' is -2.
Now we can find the sum of the first four terms using the formula for the sum of a geometric series:
Sum = a * (1 - r^n) / (1 - r)
where 'n' is the number of terms.
In this case, 'n' is 4, so:
Sum = 3 * (1 - (-2)^4) / (1 - (-2))
Simplifying,
Sum = 3 * (1 - 16) / (1 + 2)
Sum = 3 * (-15) / 3
Sum = -15
Therefore, the sum of the first four terms is -15.