Final answer:
The given sequence is defined recursively with the formula an = an-1 - 5, starting with a1 = -7. Each term of the sequence can be calculated using the recursive formula, and the sequence decreases by 5 each time.
Step-by-step explanation:
The given sequence is defined recursively by the equation an = an-1 - 5, with the initial value a1 = -7.
To find the terms of the sequence, we can use the recursive formula to calculate each term:
- a1 = -7
- a2 = a1 - 5 = -7 - 5 = -12
- a3 = a2 - 5 = -12 - 5 = -17
- a4 = a3 - 5 = -17 - 5 = -22
- ...
The sequence can be represented as: -7, -12, -17, -22, ...
The sequence decreases by 5 each time. So, the nth term can be found using the formula: an = a1 + (n-1)(-5)