Sequence and Series

A sequence of integers A(1) + A(2) + …. + A(n) satisfies A(n – 2) = A(n + 1) – A(n) for n > 1. suppose the sum of first 999 terms is 1003 and the sum of first 1003 terms is 999. find the sum of the first 2002 terms.
PS: Please provide solution i dont have answer...

@just_neelansh
i feel something is missing in question can u give the printed question. please.

me too think something is missing.

I am provided with this btw what is missing..

@just_neelansh
first doubt is what is A(2)
is it second term or is it sum of first two termsis it A$_{1}$ or A(1)

its obviously a sequence like this...
A(1),A(2).....
SUM= A(1)+A(2)+..

not clear.
u mean to say
it is like a$_{1}$, a$_{2}$ and so on

@ashishdeosingh yupp its represented by a operator in between

@just_neelansh
are u sure instead of n2,n+1, n
is it n1, n+1, n or sole three consecutive terms?

quite sure

@just_neelansh
most probably question is wrong.

This post is deleted!

@ashishdeosingh but where are u struct...cant we solve this

@just_neelansh
not able to . becz terms should be mostly consecutive. else cancellations not occuring
i cud get a1003+ a1004=2003.

please provide details about source of question. if printed then atleast share this we can be sure about anything you might have missed.
is it iit level or do we need to think with IMO level concepts?

@ashishdeosingh the condition given A(n – 2) = A(n + 1) – A(n) is just for letting us know tht the sequence is in Ap as far as i approached rest is two equation given and we have to solve for first term and common difference

@nukitapuyol ...
....JEE(A)
It was also asked on a therad on FIITJEE's site same copy paste question


@just_neelansh plez provide the question link if possible

@yashkapoor provided above,
try manipulating with the terms 100 1001 1002 1003