If 1/3,a,b,c,d,e,f,g,432 are in G.P., then find the product of c and e.
(a)(ar^8) = a^2 r^8 = 432
c*e = ar^3 * ar^5 = ...
oops. (1/9)(432)
This question answer 144 how it possible
Well, you just didn't catch my typo.
c*e = (1/3)r^3 * (1/3)r^5
= (1/3)* (1/3)r^8
= (1/3)(432)
= 144
So, my correction was wrong. Clearly you did not examine my work to see where the mistake was made. You just threw up your hands and complained I was wrong. Bad form, I must say. The mistake was not hard to find.
To find the product of c and e in a geometric progression (G.P.), we need to determine the common ratio of the progression.
In a G.P., each term is obtained by multiplying the previous term by a common ratio. Therefore, to find the common ratio, we can divide any term by its preceding term.
Let's consider the terms given: 1/3, a, b, c, d, e, f, g, 432.
To find the common ratio, we can choose any two consecutive terms. Let's take the ratio of b and a:
b/a = (1/3) / a
Simplifying this gives:
b/a = 1 / (3a)
To maintain the geometric progression, c/e must also be equal to the common ratio:
c/e = 1 / (3a)
Now, we have an expression for c/e in terms of a. However, we need more information to determine the exact value of the product c * e.
If additional information regarding the values of a, b, or any other term is provided, we can substitute those values into the expression. Without further information, it is not possible to determine the product of c and e.