If $- f (x) + f (x - 1) = 3 x$ $-f(x) + f(x-1) = 3x$ and $f (1) = 1000$ $f(1)=1000$ , what is $f (20)$ $f(20)$ ?

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Answer 1 · 2016-07-12T09:48:27

$f (20) = 373$ $f(20)=373$

Given

$-f(x)+f(x-1)=3x...(1)" And "f(1)=1000$

$"Putting", x=1 " in "(1) "we have"$

$=>-f(1)+f(1-1)=3*1$

$=>-1000+f(0)=3$

$=>f(0)=1003$

$"Now putting "x=1,2,3,...20 " in "(1)" we get"$

$cancel(-f(1))+f(0)=3*1$

$cancel(-f(2))+cancel(f(1))=3*2$

$cancel(-f(3))+cancel(f(2))=3*3$

$cancel(-f(4))+cancel(f(3))=3*4$
$................$
$................$
$................$

$-f(20)+cancel(f(19))=3*20$

So adding above last 20 equations we finally get

$-f(20)+f(0)=3(1+2+3+....+20)$

$=>-f(20)+1003=3*20/2(20+1)$

$=>-f(20)+1003=630$

$=>f(20)=1003-630=373$

If -f(x) + f(x-1) = 3x−f(x)+f(x−1)=3x-f(x) + f(x-1) = 3x and f(1)=1000f(1)=1000f(1)=1000, what is f(20)f(20)f(20) ?