The recursive sequence that would produce the sequence 8,-35,137,… is T(n + 1) = -3 - 4T(n) where T(1) = 8
How to determine the recursive sequence that would produce the sequence?
The sequence is given as:
8,-35,137,…
From the above sequence, we can see that:
The next term is the product of the current term and -4 added to -3
i.e.
Next term = -3 + Current term * -4
So, we have:
T(n + 1) = -3 + T(n) * -4
Rewrite as:
T(n + 1) = -3 - 4T(n)
Hence, the recursive sequence that would produce the sequence 8,-35,137,… is T(n + 1) = -3 - 4T(n) where T(1) = 8
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