Visitor

2016-04-26 07:13:13

#1

In an arithmetic progression sixth term equals 3, and progression ratio is greater than 0.5. ratio for progression to be the product of the first, fourth and fifth termen of progression is greatest.

Visitor

2016-04-26 07:15:17

#2

I suppose that termen = term

Am I right?

Am I right?

Visitor

2016-04-26 07:36:30

#3

We suppose that we have the following **arithmetic progression**: (a_{n}) with:

a_{1} = a (first therm)

q = ratio, and q > 0.5

a_{6} = a + 5q => a_{1} = a_{6} - 5q = 3 - 5q

a_{4} = a + 3q => a_{4} = 3 - 2q

a_{5} = 3 - q

So, we have

a_{1} * a_{4} * a_{5} = (3-5q)(3-2q)(3-q) = -10 q^{3} + 51 q^{2} - 72 q + 27.

We derive this expression to find points of maximum or minimum. If we derive we obtain:

-30 q^{2} + 102 q - 72 = 0

If we solve this second grade equation we obtain

q_{1} = 1

q_{2} = 2.4

Both of them are good for us because them are bigger than 0.5

a

q = ratio, and q > 0.5

a

a

a

So, we have

a

We derive this expression to find points of maximum or minimum. If we derive we obtain:

-30 q

If we solve this second grade equation we obtain

q

q

Both of them are good for us because them are bigger than 0.5

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