Recursive Definition

**oldguy** · November 21st 2007, 05:52 PM

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.

**CaptainBlack** · November 21st 2007, 08:42 PM

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.

$<br /> A_n=(n+1)/3<br />$

$<br /> A_{n-1}=n/3<br />$

so:

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

RonL

**Soroban** · November 22nd 2007, 05:12 AM

Hello, oldguy!

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

Crank out the first few terms . . .

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

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

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

**oldguy** · November 22nd 2007, 05:55 AM

Thanks, Oldguy

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