The explicit rule of the sequence is (d) [tex]a_n = 8-6 (n -1)[/tex]
How to determine the explicit formula?
The sequence is given as:
a1 = 8
[tex]a_n = a_{n-1} - 6[/tex]
Set n = 2
[tex]a_2 = a_{1} - 6[/tex]
This gives
a2 = 8 - 6
a2 = 2
Calculate the common difference (d)
d = a2 - a1
This gives
d = 2 - 8
Evaluate
a = -6
The explicit formula is then calculated as:
[tex]a_n = a_1 + (n -1)d[/tex]
This gives
[tex]a_n = 8-6 (n -1)[/tex]
Expand
[tex]a_n = 8-6n +6[/tex]
Evaluate the like terms
[tex]a_n = 14-6n[/tex]
Hence, the explicit rule of the sequence is (d) [tex]a_n = 8-6 (n -1)[/tex]
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