1. ## arithmetic progression

I have an arithmetic progression a1, a2, a3,a4,a5...Now, I have:a1=1a2=2a(x)=5a(x-2)+3a(x-1)for x=3,4,5,6,7...How can I check, that there isn't a(n) [for n>2 or n=2)] which divided a(n+2)*a(n+1)

2. Hello, Helloworld!

If no one is responding, it's because they can't read your question . . .

I have an arithmetic progression a1, a2, a3,a4,a5...Now, I have:a1=1a2=2a(x)=5a(x-2)+3a(x-1)for x=3,4,5,6,7...How can I check, that there isn't a(n) [for n>2 or n=2)] which divided a(n+2)*a(n+1)

Without spaces or commas, it's (almost) impossible to read.
Luckily, I'm a mathematical archeologist, so I can piece together a statement
. . from strange-looking fragments.

Here's what the heiroglyphics say . . .

We have an arithmetic sequence: . $a_1,\,a_2,\,a_3,\,a_4,\,\cdots$

We are given: . $a_1 = 1,\;a_2 = 2,\;\;a_n\:=\:3a_{n-1} + 5a_{n-2}$

. . First term is 1; the second term is 2.
. . Every successive term is 3 times the preceding term plus 5 times the second preceding term.

We are to prove that $a_n$ does not divide $(a_{n+1})(a_{n+2})$

. . A term does not divide the product of the next two terms.

Anyone care to give it a try?