# Recursive Definition

• Nov 21st 2007, 05:52 PM
oldguy
Recursive Definition
Question :
Give a recursive definition (with initital condition(s) of {An} (n=1,2,3 ...)

An = (n+1)/3

I am not sure how to type "A sub n" (An) in this editor.
• Nov 21st 2007, 08:42 PM
CaptainBlack
Quote:

Originally Posted by oldguy
Question :
Give a recursive definition (with initital condition(s) of {An} (n=1,2,3 ...)

An = (n+1)/3

I am not sure how to type "A sub n" (An) in this editor.

$\displaystyle A_n=(n+1)/3$

$\displaystyle A_{n-1}=n/3$

so:

$\displaystyle A_n=n/3 + 1/3 = A_{n-1}+1/3$

RonL
• Nov 22nd 2007, 05:12 AM
Soroban
Hello, oldguy!

Quote:

Give a recursive definition of $\displaystyle \{A_n\}$ with initial conditions.
. . $\displaystyle A_n \:=\:\frac{n+1}{3}$

Crank out the first few terms . . .

. . $\displaystyle A_1 \: = \: \frac{2}{3},\;\;A_2 \:= \:\frac{3}{3},\;\;A_3 \:=\:\frac{4}{3},\;\;A_4 \:=\:\frac{5}{3},\;\;\cdots$

We see that the first term is: .$\displaystyle A_1 \:=\:\frac{2}{3}$
. . and each successive term is $\displaystyle \;\frac{1}{3}$ more than its predecessor.

Therefore: . $\displaystyle A_1 = \frac{2}{3}\;\;\text{ and }\;\;A_{n+1} \:=\:A_n + \frac{1}{3}$

• Nov 22nd 2007, 05:55 AM
oldguy
Thanks, Oldguy