Answer:
a(n) = 10 -3n
Explanation:
You want the explicit formula for the sequence recursively defined by a(1)=7, a(n)=a(n-1) -3.
Common difference
The recursion relation tells you that each term is 3 less than the one before. That is, the common difference between terms is -3.
Explicit formula
A sequence with a common difference is an arithmetic sequence. The formula for the n-th term is ...
a(n) = a(1) +d(n -1)
where a(1) is the first term and d is the common difference.
The first term is given by the recursive definition as 7. Then the explicit formula is ...
a(n) = 7 -3(n -1)
This can be simplified to ...
a(n) = 10 -3n