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

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In a sequence of integers , A(n)=A(n-1)-A(n-2), where A(n) is the n'th term in the sequence, n is an integer and n>=3,A(1)=1,A(2)=1
Calculate S(1000), where S(1000)is the sum of the first 1000 terms
a)2
b)3
c)4
d)0

Asked In TCS krishnaprasad TATA (11 years ago)

Unsolved Read Solution (17)

Is this Puzzle helpful?   (28)   (10) Submit Your Solution Co-ordinate geometry

Read Solution (17) :

anish singhal  (11 years ago)

actually answer is 1...
consider the soln...
given A(1)=1,A(2)=1.
so, A(3)=A(2)-A(1) acc to the given formula A(n)=A(n-1)-A(n-2)
A(3)=1-1=0.
similarliy,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.
after 6th term seq is repeating like...1,1,0,-1,-1,0...after every 6 terms
so the sum of these 6 terms are 1+1+0+(-1)+(-1)+0=0.
now we have to find sum of 1000 terms...now consider in splitted pattern,like
sum of first 600 terms is 0...(as consider 1,1,0,-1,-1,0 as one sequence,now consider 166 seq i.e 166*6=996 terms)
so the sum of first 996 terms is 0...after that 4 terms come i.e 1,1,0,-1
so the sum of last 4 terms = 1+1+0+(-1)=1.
so according to me 1 is answer....
plzzz give ur feedback

Is this solution Helpfull? Yes (264) | No (22)  

Yash Ajmera  (11 years ago)

Ans. 1 (Not in Option)

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
And so on.... we can clearly see that After every n/6 sum of n no become 0

So till S(996) total will be 0
A(997)=1
A(998)=1
A(999)=0
A(1000)=-1
So S(1000) = 1

Is this solution Helpfull? Yes (23) | No (3)  

meena  (11 years ago)

answer is 0.
given A(1)=1,A(2)=1.
so, A(3)=A(2)-A(1) acc to the given formula A(n)=A(n-1)-A(n-2)
A(3)=1-1=0.
similarliy,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.
after 6th term seq is repeating like...1,1,0,-1,-1,0...
996th term is 6th term(due to repetetion),1000 th term is 4th one.i.e..-1.
it is in A.P.s(n)=(n/2)(a+l)where l is last term,a is 1st term.
(1000/2)(1-1)=0.
k....0 is tje answer.

Is this solution Helpfull? Yes (13) | No (26)  

Kabirul Islam  (11 years ago)

actual answer should 1 according to math calculation but according to open seesame answer will be 3......
how it would be i dnt knw......

Is this solution Helpfull? Yes (10) | No (4)  

anish singhal  (11 years ago)

@ divyank and aashly.....we have to find sum of first 1000 terms instead of 1000th term.....read question again carefully....

Is this solution Helpfull? Yes (9) | No (7)  

Divyank  (11 years ago)

if u calculate A(8)=0
A(16)=0
..
..
..
A(1000)=A(8*125)=0
as the series is repeating

Is this solution Helpfull? Yes (8) | No (30)  

Aashly  (11 years ago)

trial and error
now 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(1000)=0
so sum is 0

Is this solution Helpfull? Yes (7) | No (37)  

Swati  (11 years ago)

but 1 is not even in one of the options of openseesame test of tcs.

Is this solution Helpfull? Yes (7) | No (3)  

santhosh  (11 years ago)

finally tell any one answers yar... so many confusions...

Is this solution Helpfull? Yes (5) | No (6)  

Dipak Liladhar Patil  (10 years ago)

ans is 1.
sum of first 6 terms is 0
sum of next 6 terms is 0
likewise

1000%6 = 4
last four terms are 1,1,0,-1
hence ans is=1.

Is this solution Helpfull? Yes (3) | No   

Atul Priya Baranwal  (11 years ago)

-1
A(1000)=A(1999)-A(1998)
A(1999)=A(1998)-A(1997)
.
.
A(4)=A(3)-A(2)
A(3)=A(2)-A(1)............sum up all terms
-------------
A(1000)=-A(1)
=-1(ans)

Is this solution Helpfull? Yes (2) | No (7)  

Palash Bansal  (10 years ago)

here,,it is mentioned that no. of terms are 1000 whose sum have to be calculated and n>=3 so terms will start from 3 to 1003 instead of 1->1000
hence, 0,-1,-1,0,1,1 so sum of 6 terms is 0
therefore..sum of first 996 terms will be 0 as 996 is divisible by 6
now last 4 terms are 0,-1,-1,0
sum = -2

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

MEGHNA BARANWAL  (9 years ago)

the answer of this question should be -1
also the options in the question are wrong

Is this solution Helpfull? Yes | No   

Adam Levine  (8 years ago)

actually answer is 0...
consider the soln...
given A(1)=1,A(2)=1.
so, A(3)=A(2)-A(1) acc to the given formula A(n)=A(n-1)-A(n-2)
A(3)=1-1=0.
similarliy,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)=0-(-1)=1
A(8)=1-0=1
after 6th term seq is repeating like...0,-1,-1,0,1,1,0,-1,-1,0,1,1,0,-1...and so on....
REMEMBER, n>=3 ...so n starts from 3. NOT from 1. so the 1000th term is A(1003)
so now the sum of the first 6 terms are 0+(-1)+(-1)+0+1+1=0.
So, sum of 996 terms is also 0. so A(999)=0
now the next 4 numbers in the series are-- 0,-1.-1.0
so the sum upto A(1003) i.e. 1000 terms starting from n=3 is (-2)

Is this solution Helpfull? Yes | No   

SINJAN  (8 years ago)

We have A(n) = A(n-1)-A(n-2)
also given are A(1)=A(2)=1
so, A(3) will come as 0
A(4)=-1
A(5)=-1
and A(6)= 0

Sum of first 6terms, that is from A(1)+A(2)+...+A(6)= 1+1+0-1-1+0=0
SO, SUM OF FIRST 600 TERMS = 0
SO SUM OF FIRST 996 TERMS (as 996 is the last number before 1000 that is a multiple of 6 ) = 0
Now repeating the cycle we get ,

A(997)=1
A(998)=1
A(999)=0
A(1000)=-1

NOW...

A(1000) = A(999) - A(998)
A(999) = A(998) - A(997)
A (997) = A(996)-A(995) NOTICE THAT A(998), A(997), A(996),A(995) AND SO ON WILL GET CANCELLED
.
.
.
A(5) = A(4) - A(3)
A(4)= A(3)-A(2)
A(3)=A(2)-A(1)
------------------------------------------------

WE SEE AT THE END OF THE SERIES OF SUM WE HAVE ONLY A(999)-A(1) AS THE REST OF THE NUMBERS GET CANCELLED.
WE KNOW A(999)= 0 AND A(1) = 1
SO A(999)-A(1) = 0-1 = -1 ANSWER.

PLEASE GIVE FEEDBACK GUYS!!

Is this solution Helpfull? Yes | No (1)  

J E Tejeswar Gowd  (8 years ago)

for every completion of 6 terms the series is repeating so, the greatest 3 digit number that is divisible by 6 is 996
i.e., upto 996 the sum =0
rest of the series is 1,1,0,-1
so, sum=1+1+0-1=1
But answer is not found in the option.

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arundhati sen  (6 years ago)

ans:1
not in option

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