If -f(x) + f(x-1) = 3xf(x)+f(x1)=3x and f(1)=1000f(1)=1000, what is f(20)f(20) ?

1 Answer
Jul 12, 2016

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

Explanation:

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
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-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