# Arithmetic Progression

Cameron
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.

## RE: Arithmetic Progression

Steve
Visitor
2016-04-26 07:15:17
#2
I suppose that termen = term

Am I right?

## RE: Solving Maximim of the prducts of terms of Arithmetic Progression

Steve
Visitor
2016-04-26 07:36:30
#3
We suppose that we have the following arithmetic progression: (an) with:
a1 = a (first therm)
q = ratio, and q > 0.5
a6 = a + 5q => a1 = a6 - 5q = 3 - 5q
a4 = a + 3q => a4 = 3 - 2q
a5 = 3 - q

So, we have
a1 * a4 * a5 = (3-5q)(3-2q)(3-q) = -10 q3 + 51 q2 - 72 q + 27.

We derive this expression to find points of maximum or minimum. If we derive we obtain:
-30 q2 + 102 q - 72 = 0
If we solve this second grade equation we obtain
q1 = 1
q2 = 2.4

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

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