Answer:
Option (C)
Step-by-step explanation:
Recursive formula of sequence is,
[tex]a_1=-7[/tex]
[tex]a_n=a_{n-1}-5[/tex]
Therefore, sequence will be in the form of,
-7, -12, -17,......
Therefore, common difference of the given arithmetic sequence,
d = [tex]a_n-a_{n-1}[/tex]
= -5
Explicit formula for an arithmetic sequence is,
f(n) = a + (n - 1)d
where a = first term of the sequence
n = nth term
d = common difference in each successive term
By substituting the values from the sequence,
f(n) = -7 + (n - 1)(-5)
= - 7 - 5(n - 1)
= -7 - 5n + 5
f(n) = -5n - 2
Option (C) will be the correct option.
