if 1^2+2^2+3^2+4^2+........... +1000^2 = A and 1^2+2^2+3^2+4^2+...........+500^2 = B then 1^2+3^2

M4maths Previous Puzzles

20 Mar 2012 solve

if 1^2+2^2+3^2+4^2+........... +1000^2 = A
and 1^2+2^2+3^2+4^2+...........+500^2 = B
then 1^2+3^2+5^2+..............+999^2 = ?

OPtion

1) A-B
2) A-2B
3) A+B
4) A+2B
5) A-3B
6) A+3B
7) 2A+3B
8) 2A-3B
9) A-4B
10) none of these

Solution

A = 1^2+2^2+3^2+4^2+.........+1000^2
A = [1^2+3^2+5^2+........+999^2] + [2^2+4^2+........+1000^2]
A = ? + 2^2 [ 1^2+2^2+3^2+4^2+...........+500^2]
A = ? + 4 B
so ? = A - 4B

Correct Option: 9 Best Solution (0)