Final answer:
The first five terms of each sequence are generated by identifying the pattern of the sequence. The first sequence increases by 5 for each term, while the second and third sequences involve variations of arithmetic progressions with operations alternating between subtraction and addition.
Step-by-step explanation:
The question asks for writing the first five terms of the sequence for each series of numbers provided. We will address the sequences given, one at a time.
- For the sequence 5, 10, 15, 20, the pattern is that each term increases by 5. So the first five terms are 5, 10, 15, 20, 25.
- The sequence −1, −8, −7, −2, −9, −15, −18, −20 seems to be two interleaved arithmetic sequences. The first alternates between subtraction of 7 and addition of 1. The first five terms following this pattern would be −1, −8, −7, −2, −9. The second alternates between subtraction of 7 and subtraction of 2. Its first five terms would be −21, −29, −34, −36, −44.
- For the sequence −44, −59, −73, −82, −84, the pattern is that each term is the previous term subtracted by an incrementally increasing number. The sequence progresses by subtracting 15, then 14, 13, and so on. Following this pattern, the first five terms are −44, −59, −73, −82, −84.
It seems there is a portion of the text referring to a constant involving exponents (5-6-7-8) and geometric probability related to five games. However, these do not appear to be directly related to generating the sequence terms, so they will not be included in the answer.