# Thread: Arithmetic and geometric sequence

1. ## 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

2. Hello,

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

You've stated the equations correctly !

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

3. yea i know that, but i don't have k nor d..