Latest TCS Aptitude Question SOLUTION: In a sequence of integer A(n)=A(n-1)-A(n-2)where A(n) is nth term, n is integer and n>=3,A(1)=1,A(2)=1,calculate S(1000)

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In a sequence of integer A(n)=A(n-1)-A(n-2)where A(n) is nth term, n is integer and n>=3,A(1)=1,A(2)=1,calculate S(1000)

Asked In TCS gayathri k (10 years ago)

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RAKESH  (10 years ago)

A(n)=A(n-1)-A(n-2)
A(1)=1
A(2)=1
A(3)=A(3-1)-A(3-2)=A2-A1=1-1=0
A(4)=A3-A2=0-1=-1
A(5)=A4-A3=-1-0=-1
A(6)=A5-A4=-1-(-1)=0
A(7)=A6-A5=0-(-1)=1
A(8)=A7-A6=1-0=1
A(9)=A8-A7=1-1=0
A(10)=A9-A8=0-1=-1 .... so on


we see that series is repeating after 1st 6 terms

sum of 1st 6 terms=1+1+0-1-1+0=0

1000=6*166+4=996+4


S(1000)=A(1)+A(2)+A(3)+....+A(1000)
=sum of ist 996 terms + last 4 terms
=[(1+1+0-1-1+0)+(1+1+0-1-1+0)+...166 times]+(1+1+0-1)
= 0+0+0+...166 times + (1+1+0-1)
=1

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aditya  (10 years ago)

gand phadu ha

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pkc  (10 years ago)

le muh me leee

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akash  (10 years ago)

Sahi bol rha h ye

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