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 integer and n>=3,a(1)=1,a(2)=1 then calculate s(1000) where s(1000) is the sum of

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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 integer and n>=3,a(1)=1,a(2)=1 then calculate s(1000) where s(1000) is the sum of first 1000 terms

Asked In TCS vijeta dass (10 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

Vinay Jain  (10 years ago)

a(n) = a(n-1) - a(n-2)

a(3) = a(2) - a(1)
a(4) = a(3) - a(2)
a(5) = a(4) - a(3)
a(6) = a(5) - a(4)
.
.
.
.
.
a(1000) = a(999) - a(998)

Add all these equations and look carefully on adding terms are cancelling each other, so at last we will get the final expression as :-

a(1000) = -a(1)
a(1) + a(1000) = 0
Adding a(2) on both sides

a(1) + a(2) + a(1000) = a(2)

We have reached this expression by adding all the terms so the expression on left side is nothing but the value of s(1000)

so answer is s(1000) = a(2) = 1

Is this solution Helpfull? Yes (23) | No (4)  

mavuri tejaswi  (10 years ago)

we know that a(1)=1, a(2)=1
from these values we can get a(3),a(4).... and soon.
but at a(7) the cycle will repeat.
a(3)=0,a(4)=-1,a(5)=-1,a(6)=0
then 1000/6=166 with remainder 4. by adding the first four values we can get 1

Is this solution Helpfull? Yes (11) | No   

Kundan Kumar  (10 years ago)

we know that
a(1)=1,
a(2)=1
a(3)=0,
a(4)=-1
a(5)=-1
a(6)=0
but at a(7) the cycle will repeat.
Hence it has cyclicity of 6.
Now when we add,
a(1)+a(2)

a(3) = a(2) - a(1)
a(4) = a(3) - a(2)
a(5) = a(4) - a(3)
a(6) = a(5) - a(4)
.
.
.
.
.
a(1000) = a(999) - a(998)
All the terms gets cancelled excluding a(2) and a(999)
Hence s(1000)=a(2)+a(999)
using cycility of 6 we can calculate a(999)
ie. divide by 6 get the remainder
a(999)=0
Therefore,
s(1000)=a(2)+a(999)
= 1+0
s(1000)=1 ans.

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

M Sri Raviteja  (10 years ago)

ans is 1....

Is this solution Helpfull? Yes (2) | No   

Anirban  (9 years ago)

how can u say a(999)=0 ?

Is this solution Helpfull? Yes (2) | No   

narendra madhur  (10 years ago)

I want ask to vijeta that the questions are on m4 site are comes on tcs or not .if comes then please send me question papers on id naendra.madhur@gmail.com.

Is this solution Helpfull? Yes (1) | No   

Suyash Kunawat   (10 years ago)

@vinay jain. on adding the equations we will get a(3)+a(4)+.....a(1000)= -a(1)+a(999)
on adding a(1)&a(2) on both sides we get
a(1)+a)2)+a(3)+......a(1000)= a(1)+a(2)-a(1)+a(999)
s(1000)= a(2)+a(999).
if i am right please explain me further

Is this solution Helpfull? Yes (1) | No   

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