Arithmetic and geometric sequence

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• Dec 14th 2008, 05:54 AM
metlx
Arithmetic and geometric sequence
You have an arithmetic and geometric sequence. Both have 3 numbers in it. (ie. in arith. s. would be for example 2,4,6; in geo. s. would be 2,4,8;)

The 3rd number in both sequences is 24.

if you multiply the 1st number of arith. sequence and 1st number of geo. sequence you get 18.
if you multiply the 2nd number of arith. sequence and 2nd number of geo. sequence you get 108.

Write down both sequeneces..

----------------------------------
I managed to get that far:

a (letter which i use for arithm. sequences)
b (letter for geo. sequences)
(a1 = 1st number of the sequences... etc)

a3 = a1 + 2d = 24 = b1 * k^2
a1 * b1 = 18
a2 * b2 = 108

can someone please help..
• Dec 14th 2008, 06:23 AM
Moo
Hello,

Quote:

Originally Posted by metlx
You have an arithmetic and geometric sequence. Both have 3 numbers in it. (ie. in arith. s. would be for example 2,4,6; in geo. s. would be 2,4,8;)

The 3rd number in both sequences is 24.

if you multiply the 1st number of arith. sequence and 1st number of geo. sequence you get 18.
if you multiply the 2nd number of arith. sequence and 2nd number of geo. sequence you get 108.

Write down both sequeneces..

----------------------------------
I managed to get that far:

a (letter which i use for arithm. sequences)
b (letter for geo. sequences)
(a1 = 1st number of the sequences... etc)

a3 = a1 + 2d = 24 = b1 * k^2
a1 * b1 = 18
a2 * b2 = 108

can someone please help..

You've stated the equations correctly !

Now, I'm sure it would help if you consider these two new equations :
$a_2=a_1+d$
$b_2=b_1*k$

(Wink)
• Dec 14th 2008, 06:31 AM
metlx
yea i know that, but i don't have k nor d..