Aptitude - Numbers - Discussion

This sum is very easy with this formula n (n+1)*(2n+1) divide by 6 20(20+1)*(20*2+1) divided by 6 after multiplying break squares and divided with 6 then no. after multiplying dividing with 6 and subtract of both answer.

From where this come from (12 + 22 + 32 +.....+ 202) - (12 + 22 + 32 +.....+ 102).

We know that Sum of 1 square to 20 square = 2870 by the formula n/6 X (n+1) X (2n+1).

Therefore sum of 1 square to 10 square = 385.

So, the sum of 11 square to 20 square is 2870 - 385 = 2485.

10 * 11 * 21 / 6 How it came?

Please explain.

Nice explanation @Kavitha.

I didn't get a proper answer. Please, can anybody give me proper answer & shortcut.

It's very easy.
All u have to do is learn the formula.
(1^2 + 2^2 + 3^2+.......n^2) = 1/6 n(n+1)(2n+1).

So, we know the solution of above type of series so we can reduce the series given in Qns to this type of series.

So, what we are doing next is expanding the given series of question into (1^2 + 2^2+....+20^2), which will be solved by above formula 1/6 n(n+1)(2n+1) with the value n=20 and we will get 2870.

But the series in the question is only of squares of 11 to 20 so, now we will find the solution by using the same formula for squares of 1 to 10 ( by taking n=10 for this series as we are solving only up to 10 ^2) and we will get a solution of 385.

After that, we will minus 385 from 2870 and we will find a solution for the given series as 2485.

I can't understand please explain me clearly.

Numbers which starts from 1 then the sum of series formula = 1/6* n(n + 1)(2n + 1).
But in our sum which starts from 12.
So we have to find two separate sum of series.
1st one for 1 to 10.
2nd one for 11 to 20.
As per our formula,
For 1 to 10 here.

N = 10
So we get,
1/6 * 10(10+1)(2*10+1) = 385.
Like as n=20.
1/6* (20(20+1)(2*20+1) = 2485.
We have to find ans for (11^2 + 12^2 + 13^2 + ... + 20^2).
So do sub of 2485 -385 = 2485.

Thanks, I got it.