00:01
Hi, here it is given that the first term of an arithmetic series is 3 and also given that the common difference is 4 and the sum of all the terms is 820.
00:50
So, that we can write it as a equal to 3, d equal to 4 and sn equal to 820.
01:00
First we have to find the total number of terms and then we can find the last term so that the sum of n terms is given by the formula sn equal to n by 2 into 2a plus n minus 1 into d.
01:22
Here we have to substitute the values where sn is 820 which is equal to n by 2 into 2 into 3 plus n minus 1 into 4.
01:35
Here we have to find the value of n which is the number of terms.
01:40
Therefore, 820 equal to n by 2 into 6 plus 4n minus 4.
01:49
Here we have to simplify this to find the value of n.
01:52
That is 820 equal to n by 2 into 2 plus 4n.
01:57
Then by simplifying we will get 820 equal to n plus 2n square.
02:06
Then subtracting 820 on both sides we will get 2n square plus n minus 820 equals to 0.
02:17
Here we can find the value of n using the formula minus b plus or minus square root of b square minus 4ac by 2a.
02:33
Since the equation is in quadratic form, so that here from the quadratic equation we can say that a equal to 2, b equal to 1 and c equal to minus 820 such that n equal to minus 1 plus or minus square root of b square that is 1 square minus 4 into 2 into minus 820 by 2 into 2 such that it will be minus 1 plus or minus square root of 1 plus 6560 by 2.
03:22
We can write it as minus 1 plus or minus square root of 6561 by 4...