1. ## triangle sequence

Given the sequence of isosceles right triangles P to A sub n to A sub n+1
with P to A sub n+1 = A sub n to A sub n+1 and with P to A sub 1 = 1

Find the smallest value of n such that A sub n to A sub n+1 < 0.001

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To try to use formal algebraic symbolism, the process and symbolic form is tough to create; but if you have access to a BASIC language then you might find your answer through this, extremely unrefined program:

dim S(50)
i=0
input "Initial Length Hypotenuse? ";So
LET S(1)=1
LET i=1
FOR i=1 to 40
'i=i+1
S(i) = So/(sqr(2))
So=S(i)
print i;" loopwhiletest ";S(i)
i=i+1
NEXT i
END
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im only a sophmore in pre calc. i have no idea wat the above responce wanted me to do...???

2. Originally Posted by Mr_Green
Given the sequence of isosceles right triangles P to A sub n to A sub n+1
with P to A sub n+1 = A sub n to A sub n+1 and with P to A sub 1 = 1

Find the smallest value of n such that A sub n to A sub n+1 < 0.001

"""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""""""""""""""""
To try to use formal algebraic symbolism, the process and symbolic form is tough to create; but if you have access to a BASIC language then you might find your answer through this, extremely unrefined program:

dim S(50)
i=0
input "Initial Length Hypotenuse? ";So
LET S(1)=1
LET i=1
FOR i=1 to 40
'i=i+1
S(i) = So/(sqr(2))
So=S(i)
print i;" loopwhiletest ";S(i)
i=i+1
NEXT i
END
"""""""""""""""""""""""""""""""""""""""""""""""""" """"""""""""

im only a sophmore in pre calc. i have no idea wat the above responce wanted me to do...???
$\displaystyle A_{n+1}=A_n/\sqrt{2}$

and $\displaystyle A_1=1$, so:

$\displaystyle A_n=\frac{1}{2^{(n-1)/2}}$

Now set:

$\displaystyle A_n=\frac{1}{2^{(n-1)/2}}=0.001$

Taking logs:

$\displaystyle -\frac{n-1}{2}\log_{10}(2) = \log_{10}(0.001)=-3$

so:

$\displaystyle n=-\frac{3 \times 2}{\log_{10}(2)}+1 \approx 20.93$

To get the smallest integer so that $\displaystyle A_n<0.001$ we need to
round this up to $\displaystyle n=21$.

RonL