Answer:
Step-by-step explanation:
You want explicit and recursive formulas for the arithmetic sequence that begins -1.5, -7.5, -13.5, -19.5, ....
The sequence has a first term of a1 = -1.5.
The common difference between successive terms is d = -7.5 -(-1.5) = -6.
The explicit formula for n-th term an is ...
an = a1 +d(n -1)
For the values of a1 and d here, the formula is ...
an = -1.5 -6(n -1)
The recursive formula comes in two parts. The first part specifies an initial condition:
a(1) = a1
The second part specifies how the next term is found from the last:
a(n) = a(n-1) +d
For the values of a1 and d here, the formula is ...
a(1) = -1.5; a(n) = a(n-1) -6
The domain of the recursive function is n ≥ 2.
