Latest TCS Aptitude Question SOLUTION: In a sequence of integers, A(n)= A(n-1) – A(n-2), where A(n)is the nth term in the sequence, n is an and n>=3, A(1)=1,A(2)=1. Calculate S(1000), where S(1000) is the sum of the f

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In a sequence of integers, A(n)= A(n-1) – A(n-2), where A(n)is the nth term in the sequence, n is an and n>=3, A(1)=1,A(2)=1. Calculate S(1000), where S(1000) is the sum of the first 1000 terms.Options:
-1
0
2
1

Asked In TCS SUDIP ROY (10 years ago)

Unsolved Read Solution (11)

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karthikeyank  (10 years ago)

ANS:1
A(3)=A(2)-A(1)=1-1=0
A(4)=A(3)-A(2)=0-1=-1
A(5)=A(4)-A(3)=-1-0=-1
A(6)=A(5)-A(4)=-1+1=0
A(7)=A(6)-A(5)=0+1=1
A(8)=A(7)-A(6)=1-0=1
A(9)=A(8)-A(7)=1-1=0
A(10)=A(9)-A(8)=0-1=-1
Ex:S(10) Terms result=> 1+1+0-1-1+0+1+1+0-1=1
hence S(1000)=1

Is this solution Helpfull? Yes (24) | No (1)  

khushboo  (10 years ago)

A(1)=1
A(2)=1
A(3)=1-1=0
A(4)=0-1=-1
A(5)=-1-0=-1
A(6)=-1+(-1)=0
A(7)=0+1=1
A(8)=1-0=1
so we can see that after 6 terms we get zero
A(997)=1
A(998)=1
A(999)=0
A(1000)=-1
hence S(1000)=1
ans=1

Is this solution Helpfull? Yes (15) | No (2)  

NEERAV NIKUNJ  (10 years ago)

A(1)=1
A(2)=1
A(3)=1-1=0
A(4)=0-1=-1
A(5)=-1-0=-1
A(6)=-1+(-1)=0
A(7)=0+1=1
A(8)=1-0=1

Here we can see that after every 6 terms series is repeating.
And the sum of every 6 terms is 0 .. SO,
S(996)=0;
S(1000)=S(996)+1+1+0-1
Which is equal to 1
Ans= 1

Is this solution Helpfull? Yes (4) | No   

Sindhuja  (10 years ago)

sol:1
A(3)=A(2)-A(1)=1-1-0
similarly,
A(4)=-1;
A(5)=-1;
A(6)=0
the ans goes as,1 1 0 -1 -1 0 1 1 0...........
addition of 6 terms is 0.
s(1000)=996+4=0+(1+1+0+(-1))=1

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shalvi mithal  (10 years ago)

Answer : 0
The sequence would be 1 1 0 -1 -1 1 1 0 -1 -1
so sum would be 0

Is this solution Helpfull? Yes (2) | No (3)  

Sarthi Chugh  (10 years ago)

1 is answer
Sequence formed: 1,1,0,-1,-1,0,1,1....repetition after every 6 digits.
Each 6 digits have sum=0. So 1000mod6=4 digits will remain with effective sum which is:1+1+0+(-1)=1.

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venkatesh  (10 years ago)

@Khushboo because N>=3 I think s(1000)-a(1) -a(2) =1-2= -1
Dont you think this is needed?

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durga prasad  (10 years ago)

1
series is
1,-1,-2,-1,1,2,1,-1,-2,-1,1....
sum of them will be 0+1(1000th term is 1)
so s(1000)=1

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Ritika Jain  (10 years ago)

ans. =1
since on writing its terms we get: 1,1,0,-1,-1,0,1,1,0...
as we can see sum of six consecutive digits is 0 and dividing 1000 by 6 we get 4 as remainder therefore taking four terms say 1,1,0,-1 and taking their sum out we get 1 as the answer.

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prachi tyagi  (10 years ago)

series is 1,1,0,-1,-1,0,1,1,0,-1,-1,0....
so 1,1,0,-1,-1,0 repeats...
for first 1000 terms (1000/6=166.something)i.e, 166 cycles will fully complete
so 166*6=996 terms will have sum 0 as sum of each cycle is 0(-1+-1+0+1+1+0=0)
so last 4 terms will be 1,1,0,-1 whose sum is 1.

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rahul gera  (10 years ago)

1
sum of every 6 terms is 0

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