Final Answer:
The missing terms in the given arithmetic sequence are 59, 43, and 27. This conclusion is drawn by observing a consistent pattern of decreasing multiples of 4 between consecutive terms in the sequence.
Step-by-step explanation:
In an arithmetic sequence, each term is obtained by adding a constant difference (d) to the previous term. To find the missing terms, let's analyze the differences between consecutive terms in the provided sequence.
The first difference between 63 and the next term is 63 - __ = 63 - __ = 63 - 55 = 8. The second difference is 55 - __ = 55 - 51 = 4. Notice that the differences are decreasing by 4 each time. This pattern implies a common difference (d) of -4.
Now, applying this common difference to find the missing terms:
Starting from 63, subtracting 4 repeatedly gives us 59, __, __, 43, __, __, 27, and so on.
Therefore, the missing terms in the sequence are 59, 43, and 27. This is supported by the consistent pattern of subtracting 4 to obtain each subsequent term in the sequence.
The arithmetic progression is governed by the formula a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term in the sequence, and d is the common difference. In this case, a_1 = 63, and d = -4, resulting in the correct determination of the missing terms.