Hello!
The recursive rule for an arithmetic sequence: [tex] a_{n} = a_{n-1} + d [/tex].
The explicit rule for an arithmetic sequence: [tex] a_{n}=a_{1} +d(n-1) [/tex].
[tex] a_{n} [/tex] is the value you are trying to find, or simply the answer. :)
[tex] d [/tex] is the common difference of the sequence.
[tex] a_{1} [/tex] is the first term of the sequence.
Given, [tex] a_{1} = 8 [/tex] and [tex] a_{n}=a_{n-1} - 6 [/tex]...
The common difference is -6, and the first term is 8.
Plug these values into the explicit rule for an arithmetic sequence, you get:
[tex] a_{n}=8+(-6)(n-1) [/tex].
Therefore, the answer is A, [tex] a_{n}=8+(n-1)(-6) [/tex].
If you wondered why, [tex] a_{n}=8+(-6)(n-1) [/tex] is equal to [tex] a_{n}=8+(n-1)(-6) [/tex], the Commutative Property of Multiplication states that when two numbers are multiplied together, the answer is the same regardless of the order of the numbers, which makes [tex] a_{n}=8+(-6)(n-1) [/tex] and [tex] a_{n}=8+(n-1)(-6) [/tex] equal to each other.
