Math Is Fun Forum

coolbee

Member

Registered: 2016-04-05

Posts: 19

questions on progression

If x ∈ R, the numbers

form an A.P. , then find the interval in which a must lie.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: questions on progression

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: questions on progression

I agree with thickhead, provided that the order of the progression is that given.

For the fun of it:
If the order is 5^(1+x)+5^(1-x), 25^x+25^-x, a/2
Or a/2, 25^x+25^-x, 5^(1+x)+5^(1-x)
Then "a" is not less than -12.

If a/2, 5^(1+x)+5^(1-x), 25^x+25^-x
Or 25^x+25^-x, 5^(1+x)+5^(1-x), a/2
Then "a" is not greater than 54.

Last edited by Relentless (2016-04-27 21:59:32)

coolbee

Member

Registered: 2016-04-05

Posts: 19

Re: questions on progression

can you please elaborate.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: questions on progression

Hi (:

If we substitute and simplify, into either equation, we just get:

The minimum of this "function", when x is 0, is 12.

Last edited by Relentless (2016-04-28 17:13:18)

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: questions on progression

What about the other two " for the fun of it"?

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: questions on progression

Hey (:

I'm going to set

and

So, for example, for the original problem:

For further example, if we were to order the terms the opposite way, we would get:

For the first paragraph (p,q,a/2 or a/2,q,p):

Or:

For the second paragraph (a/2,p,q or q,p,a/2):

Or:

which is a more difficult expression, but turns out to have a maximum of 54 when x is positive or negative a logarithmic expression near 0.974

Last edited by Relentless (2016-04-28 19:38:01)

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: questions on progression

Last edited by thickhead (2016-04-29 02:26:03)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

coolbee

Member

Registered: 2016-04-05

Posts: 19

Re: questions on progression

nice. thanks

here is one more question:

If

,
then

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: questions on progression

Last edited by thickhead (2016-04-30 04:26:09)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: questions on progression

Hi;

That is a nice answer but you might have to state that it is only valid for k>=2.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: questions on progression

I just overlooked it.but then I have to state the values not available in the eqation.

Last edited by thickhead (2016-04-30 18:04:58)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}