Just give a Try

When we observe the unit digit of squares we observe a striking pattern.

1,4,9,16,25,36,49,64,81.

Let us observe the units digit of the first 9 squares.

1,4,9,6,5,6,9,4,1.

It is a palindrome and the sum is equal to 45.

Square of every multiple of 10 will end with a zero.

Moreover, the unit digit of squares only depends on the unit digit of the number itself.

So, we can see a repetition of this sequence with a period of 10.

So, the sum of the unit digits of the sequence will be 45 x 90 which ends with a zero.

However, the best method to this is to use the series formula.

$\frac { n(n+1)(2n+1) }{ 6 }$ .

Here, n = 1000. So, it becomes.

$\frac { 1000(1000+1)(2\times 1000+1) }{ 6 } \quad =\quad 500\times 1001\times 667$ .

Which always ends in a zero which is the units digit.