Sequences

Ilsa · #1 $Old$ November 20th, 2009, 08:45 AM

There are two infinite sequences:

(an)n≥1 : 1∙1, 2∙3, 3∙5, 4∙7,……..

(bn)n≥1 : 1∙3, 2∙5, 3∙7, 4∙9,……..

Find general formulae for the two sequences and find how many common elements they have.

Drexel28 · #2 $Old$ November 20th, 2009, 09:21 AM

Quote:

Originally Posted by Ilsa $View Post$

There are two infinite sequences:

(an)n≥1 : 1∙1, 2∙3, 3∙5, 4∙7,……..

(bn)n≥1 : 1∙3, 2∙5, 3∙7, 4∙9,……..

Find general formulae for the two sequences and find how many common elements they have.

$a_n=n\cdot(2n-1)$ and $b_n=n\cdot (2n+1)$

Grandad · #3 $Old$ November 20th, 2009, 10:08 AM

Hello Ilsa

Quote:

Originally Posted by Ilsa $View Post$

There are two infinite sequences:

(an)n≥1 : 1∙1, 2∙3, 3∙5, 4∙7,……..

(bn)n≥1 : 1∙3, 2∙5, 3∙7, 4∙9,……..

Find general formulae for the two sequences and find how many common elements they have.

The $n^{th}$ term in sequence $a_i$ is the product of $n$ and the $n^{th}$ odd number. So $a_n =n(2n-1)$ .

The $n^{th}$ term in sequence $b_i$ is the product of $n$ and the $(n+1)^{th}$ odd number. So $b_n =n(2n+1)$ .

Suppose the $n^{th}$ term in the sequence $a_i$ is equal to the $m^{th}$ term in the sequence $b_i$ . Then