Answer:
an = 7 -3(n -1)
Step-by-step explanation:
You want the formula for the n-th term of the arithmetic sequence 7, 4, 1, -2, ....
An arithmetic sequence has a first term (a1) and a common difference (d) found by subtracting the previous term from the current term.
In the given sequence, the first term is a1=7, and the common difference is d=(a2 -a1) = 4 -7 = -3.
The n-th term of the given arithmetic sequence is ...
[tex]a_n=a_1+d(n-1)\\\\\boxed{a_n=7-3(n-1)}[/tex]
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Additional comment
The formula can be simplified to ...
an = 10 -3n