The sum of the same items means that the number of items added is the same, for example, three items are the same, and adjacent means adjacent. For example, the first term is the sum of 1, 2 and 3, the second term is the sum of adjacent 4, 5 and 6, and the third term is the sum of 7, 8 and 9.

(1) Because the series is arithmetic progression, the three items of 1, 2 and 3 are 3d and * * 9d less than those of 4, 5 and 6 respectively. Similarly, items 4, 5 and 6 are 3d and * * 9d less than items 7, 8 and 9. Obviously, these and arithmetic progression. If it is the sum of n terms, each corresponding term is less nd, and the difference between the two terms is n^2d, which is still a constant value, so these sums are still arithmetic progression.

(2) If the series is geometric progression, the corresponding terms are 1: q (n- 1) and 1:nq(n- 1), and the ratio is still constant, so it is still geometric progression.