The sum of the first n terms of the arithmetic sequence is 30, and the sum of the first 2n terms is 100?

The sum of the first n terms of the arithmetic sequence is 30, and the sum of the first 2n terms is 100?

Is 210, the specific method is: Sn, s2n Sn, s3n-s2n of arithmetic sequence

If the sum of the first n terms of the arithmetic sequence {an} is 30 and the sum of the first 2n terms is 100, then the sum of the first 3N terms of the arithmetic sequence {an} is 30

Let Sn = PN ^ 2 + QN
Then Sn = PN ^ 2 + QN = 30
S2n=p(2n)^2+q(2n)=100
S3n=p(3n)^2+q(3n)
Formula PN ^ 2 + QN = 30. (1)
4pn ^ 2 + 2qn = 100. (2) formula
Subtract (1) from (2)
3pn^2+qn=70
So 9pn ^ 2 + 3qn = 210
S3n=9pn^2+3qn=210

If the sum of the first n terms in the arithmetic sequence {an} is 100 and the sum of the next 2n terms is 500, then the sum of the next 3N terms is 100______ ．

Each N-term combination of the arithmetic sequence forms a new sequence, which is also the arithmetic sequence, except that the increment of the new sequence is n times that of the original sequence. If the increment of the new sequence is x, then 200 + 3x = 500, and the solution is x = 100, then the sum of the following 3N terms is 300 + (3 + 4 + 5) x = 1500