The explicit formula for the sequence -9,-3,3,9,15 is [tex]a_n[/tex] =-9+(n-1)6.
The correct option is (C).
What is explicit formula?
The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence.
Given sequence: -9,-3,3,9,15
As, the given sequence is arithmetic sequence.
So, the difference between two consecutive term is same.
i.e., (-3)-(-9)= -6, 3-(-3)= 6, and so on.
Now, the nth term is = a+(n-1)d
as, a=-9
So, [tex]a_n[/tex]= -9+(n-1)6
= -9+6n-6
= 6n-15
Hence, [tex]a_n[/tex] =-9+(n-1)6.
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