00:01
Hi here for the given question.
00:03
We need to calculate the sum of the given arithmetic series.
00:07
So here the first one is 4 plus 8 plus 12 plus 16 up to 200.
00:13
So here now we need to calculate the sum here.
00:17
We have a 1 is equal to 4 and last term is equal to 200.
00:20
So first of all, we need to find the number of terms here in this series.
00:25
So here first of all now we can observe the difference between two terms is equal to 4.
00:31
So here in our case, we know that a n is equal to a 1 plus n minus 1 multiplied with d.
00:38
So here in our case now substituting the value.
00:41
We have 200 is equal to a 1 4 plus n minus 1 multiplied with 4.
00:47
So again, we have 196 is equal to 4 n minus 4.
00:52
So this further implies here we have value as 200 is equal to 4 n.
00:57
On simplifying this we have n is equal to here.
01:07
The value of n will be 200 divided by 4 which is equal to 50.
01:14
So here we have n equals to 50.
01:16
So here in our case now, we know that formula to calculate sum sn equals to n by 2 multiplied with a plus l.
01:24
So here in our case sn is equal to 50 divided by 2 multiplied with 4 plus 200.
01:30
So calculating this value we can say that for the first sequence the sum sn is equal to 5100.
01:38
So this is our required solution for the first part.
01:41
Now similarly here we are given with another sequence second one, which is 5 plus 10 plus 15 plus 20 continued up to 300...