If the sum of the first n terms of an arithmetic sequence is 48 and the sum of the first 2n terms is 60, then the sum of the first 3N terms of an arithmetic sequence is 48 Is it 72?

If the sum of the first n terms of an arithmetic sequence is 48 and the sum of the first 2n terms is 60, then the sum of the first 3N terms of an arithmetic sequence is 48 Is it 72?

In arithmetic sequence
Sn s2n-sn s3n-s2n will also be an arithmetic sequence
therefore
48 12 S3n-48
Is an arithmetic sequence
The tolerance is - 36
be
S3n=36

Given that the sum of the first n terms of an arithmetic sequence is a and the sum of the first 2n terms is B, find the sum of the first 3N terms

2b-a
Sn = a, s2n = B, so a1 + (n-1) d = a, a1 + (2n-1) d = B solve these two equations nd = b-a
A1 = 2a-b + D, so s3n = a1 + (3n-1) d = 2a-b + D + 3nd-d = 2a-b + D + 3b-3a-d = 2b-a

In the arithmetic sequence {an}, A1 = 2, A3 = 4, if three numbers are inserted between every two adjacent terms, it will form a new arithmetic sequence with the terms of the original sequence,
(1) What is the 10th term of the original sequence
(2) What is the 29th term of the new sequence

If 3 numbers are inserted between two numbers, then there are 9 spaces between 10 items, 10 + 3 * 9 = 37
Suppose it is the nth term, N + 3 × (n-1) = 29, n = 8, which is the 8th term of the original sequence