# Math Help - [SOLVED] Fibonacci

1. ## [SOLVED] Fibonacci

Let $a$ be the $1000$th Fibonacci number; and,

Let $b$ be the $1001$st Fibonacci number.

Then, write the $1003$rd Fib. number in terms of $a$ and $b$. Simplify.

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So $F_{1000} = a, F_{1001} = b$, then

$a + b = F_{1002} = c$

And so $c+b = F_{1003}$

I doubt this is right because I'm introducing a new constant. Any ideas?

2. Originally Posted by Startbucks
I doubt this is right because I'm introducing a new constant. Any ideas?
Yes, but what is $c?$ Just $a+b,$ so you can substitute them back in.

Here is how I would write it:

$a=F_{1000},\,b=F_{1001}$

so

$F_{1003}=F_{1001}+F_{1002}=b+F_{1002}$

$=b+(F_{1000}+F_{1001})=b+(a+b)=a+2b\text.$

Edit: I saw that, Moo Too slow, but you could have left it.