A sequence question

Yes the answer is correct!!

I have found the number using Java Program.

This is the number I think its correct.

"321132499826815828452384720320970862074060782643692138282072697388735283721646581360160762436827841025561894548480898890020542623496809423664669723066980931624908775724739402394881483009611433054415348267177640331222672835631629564907858584307850508476151574891670117047739206178124320617556197699087423367414181105249300715385128794295920765953173508643733461099002087678765648760921612656571558458025510084617009128909"

The remainder is 5!!

Is there any easy procedure to find it.. I just went with programatical approach..

i must say you are genius ES...

i am trying this question from mathematics point of view but forget that the number will be too large to handle....

thank you to you people for providing the answer to compare😁.
My solution appear to be different.
For the sequence 1,2,3,5,8,.....
when divided by 8, for the 1st term remainder will be 1 since 1 cannot be divided by 8 and 2nd term will be 2,3rd term will be 3,4th term will be 5 and 5th term will be 0. I just observed the pattern actually there is not needed to add the sum for the next term than divide that number by 8. Starting from the 6th term, the remainder will be 5 because the remainder at 4th term is 5 and 5th term is 0 so what needed to do at here is to add up the previous 2 term's remainder. After that, take the sum of the remainder minus by 8, if the sum is smaller than 8 than the sum is the remainder else the remainder is the sum of the remainder of previous 2 term minus by 8.

So here is the remainder starting from 1st term.
1,2,3,5,0,5,5,2,7,1,0,1,1,2,3,5,0,5,5,2,7,1,0,1,1,..........
notice that except the first 3 term, the remainder is keep on repeating starting from 4th term until 15 term, it repeat after 12 term
so at here i create a formula
3+n(12)=2008
n=167.083
however i only take integer value of 167
3+167x12=2007
that mean starting from 3rd term after 167 times the set of the 12 number, the remainder will be 3, and further up 1 more term will be 5.

Excellent solution friend 😀