please help with progressions :)

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January 29th 2006, 09:07 AM
grimstudy

please help with progressions :)

this is a problem from a book..
..i just hope im using the right names a variables and such for things.. ehhh.. :confused:
it goes like this:
in a rising arithmetic progression, the 3rd, 7th and 17th terms are the first 3rd terms of a geometric progression. the sum of these terms is 78.
A) find the Difference of the arithmetic progression and the Quotient of the geometric progression
B) calculate the 4th term of the geometric progression,
and show it is a term in the arithmetic progression.

I am completely stuck with this, so even a hint on how to start would be good.

by the way, I didn't notice any other people asking about progressions in the past.. whats up? :confused: :rolleyes:

thanks in advance :)
January 29th 2006, 10:26 AM
ThePerfectHacker

Quote:

Originally Posted by grimstudy

this is a problem from a book..
..i just hope im using the right names a variables and such for things.. ehhh.. :confused:
it goes like this:
in a rising arithmetic progression, the 3rd, 7th and 17th terms are the first 3rd terms of a geometric progression. the sum of these terms is 78.
A) find the Difference of the arithmetic progression and the Quotient of the geometric progression
B) calculate the 4th term of the geometric progression,
and show it is a term in the arithmetic progression.

I am completely stuck with this, so even a hint on how to start would be good.

by the way, I didn't notice any other people asking about progressions in the past.. whats up? :confused: :rolleyes:

thanks in advance :)

I think you might need more infromation, did you forget something?
Or did you imply that the difference and quotient are the same. If yes then,

The difference constant is 3 and the quotient constant is 3 also.
January 30th 2006, 12:24 AM
CaptainBlack

Quote:

Originally Posted by grimstudy

this is a problem from a book..
..i just hope im using the right names a variables and such for things.. ehhh.. :confused:
it goes like this:
in a rising arithmetic progression, the 3rd, 7th and 17th terms are the first 3rd terms of a geometric progression. the sum of these terms is 78.
A) find the Difference of the arithmetic progression and the Quotient of the geometric progression
B) calculate the 4th term of the geometric progression,
and show it is a term in the arithmetic progression.

I am completely stuck with this, so even a hint on how to start would be good.

by the way, I didn't notice any other people asking about progressions in the past.. whats up? :confused: :rolleyes:

thanks in advance :)

Let the arithmetic progression be:

$\{ap_i,\ i=0, 1, .., n, ..\}=\{a,\ a+d,\ ..,\ a+(n-1)d,\ ..\}$ ,

and the geometric progression be:

$\{gp_i,\ i=0, 1, .., n, ..\}=\{u,\ uk,\ ..,\ uk^{n-1},\ ..\}$

Then we are told that:

$ap_3+ap_7+ap17=78$ ,

so:

$(a+2d)+(a+6d)+(a+16d)=78$ ,

or:

$a+8d=26\ ......\mbox{eq1}$ .

We are also told that:

$gp_1=ap_3,\ gp_2=ap_7,\ gp_3=ap_17,$

so:

$u=a+2d \ \ \ \ \ \ \ .....\mbox{eq2}$
$uk=a+6d \ \ \ \ \ .....\mbox{eq3}$
$uk^2=a+16d \ \ .....\mbox{eq4}$ .

Now these four equations are sufficient to solve for $a,\ b,\ u$ and $k$ .

RonL
January 30th 2006, 08:26 AM
grimstudy

woohoo

thanks for the help,
i've solved it using the sum equation (turned to a=26-8d)
i used the a i've found in the b**=a*c
which ultimately gave me the solution to d, from then on it's really quite simple.
thanks :)