Question

There are 2272 students in a school. All the students stand in a row, from left to right, holding a number such that the number with any student (except those at the ends) equals the sum of the numbers with the student on his immediate left and the student on his immediate right. If the numbers with the 1136th and 1137th students from the left end are – 57 and 16 respectively, then find the sum of the numbers with all the students.

Answer 1

:D
It seems the trend for any student number n
Where n is the position from the left (the leftmost student would be student#1)
Is that their number would be:
-73 if n = 1(mod 6)
-57 if n = 2(mod 6)
16 if n = 3(mod 6)
73 if n = 4(mod 6)
57 if n = 5(mod 6) and
-16 if n = 0(mod 6)
That means that after every 6 students, the subtotal is 0 :)

That means after 2268 students, the subtotal is 0, since 6 divides 2268.
2269 = 1(mod 6), that makes -73
2270 = 2(mod 6), that makes -130, or -73-57
2271 = 3(mod 6), that makes -114, or -130 + 16
2272 = 4(mod 6), that makes -41, or -114+73

I think the answer is -41 :D
Cheers :)