Final answer:
The explicit formula for the nth term of Sequence A is an = 5n - 4, and for Sequence B it is an = -2n - 1. Both sequences are examples of arithmetic sequences with their respective common differences.
Step-by-step explanation:
To find the simplified explicit formulas for the nth terms of the given sequences, we can identify the pattern and apply the formula for an arithmetic sequence.
Sequence A:
The sequence is 1, 6, 11, 16, ... which is an arithmetic sequence with a common difference of 5. The first term a1 is 1. Using the formula for the nth term of an arithmetic sequence, an = a1 + (n - 1)d, where d is the common difference, we get:
an = 1 + (n - 1) × 5
an = 5n - 4
Sequence B:
The sequence is -3, -5, -7, ... which is also an arithmetic sequence with a common difference of -2. The first term a1 is -3. Using the same formula, we get:
an = -3 + (n - 1) × (-2)
an = -2n - 1