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

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Answer 1 · 2016-07-12T09:48:27

#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#