Question

Please help -- very basic.
I'm stuck w/ some q abt recursive formula for the sequence:

Answer 1

How do I write a recursive formula for
\[\sqrt{p+q\sqrt{p+q\sqrt{p+q...}}}\](just for clarity the terms are:\[a_1=\sqrt{p+q}\]\[a_2=\sqrt{p+q\sqrt{p+q}}\]\[a_3=\sqrt{p+q\sqrt{p+q\sqrt{p+q}}}\]and I continue going like this, multiplying the very last q in \(a_{n-1}\), times \(\sqrt{p+q}\) to get the \(a_n\).

Answer 2

try \[a_{n+1}=\sqrt{p+\sqrt{a_n}}; ~~a_1={\sqrt{p+q}}\]

Answer 3

oh, that makes perfect sense....
I wasn't thinking about that form of it.

tnx

Answer 4

So,
\[a_1=p+q\]\[a_2=p+\frac{q}{p+q}\]\[a_3=p+\frac{q}{p+\frac{q}{p+q}}\]

and here the Formula is\[a_3=p+\frac{q}{a_n};~~a_1=p+q\]

Answer 5

I mean not a_3 in te last line, but a_(n+1)

Answer 6

\[a_{n+1}=p+\frac{q}{a_n};~~a_1=p+q\]

Answer 7

looks good!

Answer 8

yeah, I guess I wasn't taught properly... now I got another concept in my closet.
thanks again, and best of luck !

Answer 9

you're doing good, yw!