In the known arithmetic sequence {an}, A1 = 2, A3 = 3, if three numbers are inserted between every two adjacent terms, it will form a new sequence with the number of the original sequence, Find 1) what is the 12th item of the original sequence? 2) whether the 29th item of the new sequence is the item of the original sequence? If so, what is it?

In the known arithmetic sequence {an}, A1 = 2, A3 = 3, if three numbers are inserted between every two adjacent terms, it will form a new sequence with the number of the original sequence, Find 1) what is the 12th item of the original sequence? 2) whether the 29th item of the new sequence is the item of the original sequence? If so, what is it?

Original sequence: because A3 = a1 + 2D, d = 0.5, A2 = 2.5, A12 = a1 + 11d = 7.5
After inserting three terms: in the new sequence, set the tolerance as D1, which is represented by capital letters, A1 = A1, A5 = A2, then A5 = a1 + 4d1, so D1 = 0.125, a29 = a1 + 28d1 = 5.5
The 12th term of the original sequence is required to be the 12th term of the new sequence, so: A12 = a1 + (n-1) D1, the solution is n = 45
2) Suppose is, then a29 = a1 + (n-1) d solution: n = 8 is an integer, so the 29th item of the new sequence is the 8th item of the original sequence