Final answer:
The given series –13 + (–7) + (–1) + 5 + 11 can be defined as an arithmetic progression where each term increases by 6 from the previous term, starting from –13.
Step-by-step explanation:
The provided series is –13 + (–7) + (–1) + 5 + 11. To define the series, we look for a pattern in the differences between the terms. Starting with –13 and going to –7, we see an increase of 6. From –7 to –1, again we have an increase of 6. This pattern continues as we go from –1 to 5 (increase of 6) and from 5 to 11 (increase of 6).
This suggests that the series is an arithmetic progression where each subsequent term increases by 6 from the previous term. The formula for the nth term of an arithmetic series is a_n = a_1 + (n - 1) × d, where a_1 is the first term and d is the common difference between the terms. In this series, a_1 = –13 and d = 6. Therefore, we can define the series as a_n being the nth term of an arithmetic series where the first term is –13 and the common difference is 6.
To generate more terms in this series, we would simply continue to add 6 to the last known term.