The explicit formula for the sequence is:
an = -2-4(n-1)
To write a recursive sequence that represents this sequence, we need to find a formula for the nth term in terms of the (n-1)th term. We can do this by substituting (n-1) for n in the explicit formula:
a(n-1) = -2-4((n-1)-1)
a(n-1) = -2-4(n-2)
We can simplify this expression to get:
a(n-1) = -2-4n+8
a(n-1) = 6-4n
Therefore, the recursive formula for the sequence is:
a1 = -2 (the first term is given)
an = 6-4(n-1) for n > 1
We can check that this recursive formula generates the same sequence as the explicit formula by calculating the first few terms:
a1 = -2
a2 = 6-4(2-1) = 2
a3 = 6-4(3-1) = -2
a4 = 6-4(4-1) = -6
a5 = 6-4(5-1) = -10
We can see that these are the same values as we would get from the explicit formula.