Final answer:
To find the new center numbers after adding 15 rows to a Christmas tree pattern, one needs to calculate the total number of pieces and then the median numbers. However, the answer cannot be determined without the original number of rows or the specific numbering sequence.
Step-by-step explanation:
The question involves solving a problem related to number sequences commonly found in mathematics. The sequence appears to resemble an arithmetic sequence, where each row represents a level on the Christmas tree and presumably each level has a consecutive numbering scheme. To determine the numbers on the two center pieces after adding 15 rows, we need to figure out how many pieces there would be in total with the additional rows and then find the centermost numbers.
Let's assume the original tree had 'n' rows. Typically, a Christmas tree pattern would have one piece in the first row, two in the second, three in the third, and so on, meaning each row 'r' has 'r' pieces. For 'n' rows, the total number of pieces would be 1 + 2 + 3 + ... + n, which is the sum of an arithmetic series. The formula for this sum is (n/2)(first number + last number), which simplifies to (n/2)(n + 1) for this series.
If we had 15 more rows, we would have a total of 'n+15' rows, and the sum would be ((n+15)/2)(1 + (n+15)) for pieces. To find the center pieces for an even number of total pieces, we take half of this sum and then find two consecutive numbers around it. However, since the numbers given in the options are around 200, it seems that 'n' was originally in the range of these values, implying it could represent a much larger Christmas tree or something else.
Without the exact initial value of 'n', we cannot definitively choose among the options provided. If you have additional context or information about the initial number of rows on the tree or the numbering scheme used, please provide it so that a more accurate answer can be given.