A G.P has 6 terms. If the 3rd and 4th term are 28 and -56 respectively find common ratio, first term and the sum of the G.P.
from the given:
term(3) = ar^2 = 28
term(4) = ar^3 = -56
so ar^3/(ar^2) = -56/28
r = -2
then in ar^2 = 28
a(4) = 28
a = 7
sum(6) = a(r^6 - 1)/(r-1)
= 7((-2)^6 - 1)/(-2-1)
= 7(63/-3) = -147
check:
GP is 7, -14 , 28 , - 56 , 112, - 224
sum of that is -147
Why are you divide 24 in 8
the 8 terms of gp is 640 and the first terms is 5 find the common ration and 10 terms
help to resolve
Not what i asked was given
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To find the common ratio, first term, and the sum of the geometric progression (G.P.), we can use the formulas and information given.
Let's denote the first term as 'a' and the common ratio as 'r'. We also know that the G.P. has 6 terms.
The third term can be calculated using the formula: Tn = a * r^(n-1), where 'n' is the term number. So, the third term can be written as:
T3 = a * r^(3-1)
Given that the third term is 28, we can substitute the values:
28 = a * r^2
Similarly, the fourth term can be written as:
T4 = a * r^(4-1)
Given that the fourth term is -56, we can substitute the values:
-56 = a * r^3
Now we have a system of equations:
28 = a * r^2 --(1)
-56 = a * r^3 --(2)
To solve this system of equations, we can divide equation (2) by equation (1):
-2 = r
Now substitute this value of 'r' in either equation (1) or (2) to find 'a'. Let's substitute it in equation (1):
28 = a * (-2)^2
28 = a * 4
7 = a
So, the common ratio is -2, and the first term is 7.
To find the sum of the G.P., we can use the formula:
Sum = a * (1 - r^n) / (1 - r)
Given that the G.P. has 6 terms, we have:
Sum = 7 * (1 - (-2)^6) / (1 - (-2))
Simplifying this expression:
Sum = 7 * (1 - 64) / (1 + 2)
Sum = 7 * (-63) / 3
Sum = -441 / 3
Therefore, the sum of the G.P. is -441/3.